Word Problems Involving Triangle.

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Presentation transcript:

Word Problems Involving Triangle

Before We Start Recall How we can change

WORDS I N T O MATH

The following slides show how many words in word problems can be translated into Math Symbols. The translations shown are not always the only translations and there may be others more appropriate for each word problem you encounter. However, the examples in the next slides typify the most common translations of words into Math Symbols.

MATH WORDS = is

MATH WORDS = is of

MATH WORDS + more

MATH WORDS + more less

MATH WORDS product

MATH WORDS product quotient FRACTION

MATH WORDS sum

MATH WORDS sum difference

MATH WORDS twice

MATH WORDS Twice as many

MATH WORDS Twice as many Three times as many

MATH WORDS Twice as many Three times as many Triple

MATH WORDS Half of

MATH WORDS Half of Half as many

MATH WORDS One third of

MATH WORDS One third of A third as many

In the following slides you will find several different types of perimeter word problems. If you wish to see how to solve the problem, click on the problem and you will be taken to the solution.

RECTANGLE PROBLEMS The length of a rectangle is 3 times the width. The perimeter is 96 cm. Find the width and length. 1 The length of a rectangle is 50 meters. This is 6 meters more than twice the width. Find the width. 2 The length of a rectangular field is 18 m longer than the width. The field is enclosed with fencing and divided into two parts with a fence parallel to the shorter sides. If 216 m of fencing are required, what are the dimensions of the outside rectangle? 3

TRIANGLE PROBLEMS A triangle is isosceles, that is, it has two sides of equal length. The third side is 30 inches shorter than twice the length of each congruent side. The perimeter is 570 inches. Find the length of each side. 4 The first side of a triangle is 8 m shorter than the second side. The third side is 4 times as long as the first side. The perimeter is 26 m. Find the length of each side 5

1 Example #1

The length of a rectangle is 3 times the width. The perimeter is 96 cm. Find the width and length Click to go To List of Problems

Let x represent the width The length of a rectangle is 3 times the width. The perimeter is 96 cm. Find the width and length

Let x represent the width The length of a rectangle is 3 times the width. The perimeter is 96 cm. Find the width and length

Perimeter Let x represent the width The length of a rectangle is 3 times the width. The perimeter is 96 cm. Find the width and length Perimeter

Perimeter Let x represent the width The length of a rectangle is 3 times the width. The perimeter is 96 cm. Find the width and length Perimeter

Perimeter Let x represent the width The length of a rectangle is 3 times the width. The perimeter is 96 cm. Find the width and length Perimeter

Perimeter Let x represent the width The length of a rectangle is 3 times the width. The perimeter is 96 cm. Find the width and length Perimeter

Clearly shows that you are dividing by the same thing on both sides

Go back and read the problem

Let x represent the width The length of a rectangle is 3 times the width. The perimeter is 96 cm. Find the width and length

Let x represent the width The length of a rectangle is 3 times the width. The perimeter is 96 cm. Find the width and length

Let x represent the width The length of a rectangle is 3 times the width. The perimeter is 96 cm. Find the width and length The width is 12 the length is 36 Click to go To List of Problems

2 Example #2

The length of a rectangle is 50 meters. This is 6 meters more than twice the width. Find the width. Click to go To List of Problems

The length of a rectangle is 50 meters. This is 6 meters more than twice the width. Find the width.

Let w represent the width The length of a rectangle is 50 meters. This is 6 meters more than twice the width. Find the width.

50 Let w represent the width The length of a rectangle is 50 meters. This is 6 meters more than twice the width. Find the width. 50

50 Let w represent the width The length of a rectangle is 50 meters. This is 6 meters more than twice the width. Find the width. 50

50 Let w represent the width The length of a rectangle is 50 meters. This is 6 meters more than twice the width. Find the width. 50

50 Let w represent the width The length of a rectangle is 50 meters. This is 6 meters more than twice the width. Find the width. 50

Symmetric Prop. Of Equality Not Absolutely Necessary but it’s nice to have the unknown variable on the left side

Clearly shows that you are subtracting the same thing from both sides

Clearly shows that you are dividing by the same thing on both sides

Go back and read the problem

Let w represent the width The length of a rectangle is 50 meters. This is 6 meters more than twice the width. Find the width. The width is 22 meters Click to go To List of Problems

3 Example #3

The length of a rectangular field is 18 m longer than the width The length of a rectangular field is 18 m longer than the width. The field is enclosed with fencing and divided into two parts with a fence parallel to the shorter sides. If 216 m of fencing are required, what are the dimensions of the outside rectangle? Click to go To List of Problems

Let w represent the width The length of a rectangular field is 18 m longer than the width. The field is enclosed with fencing and divided into two parts with a fence parallel to the shorter sides. If 216 m of fencing are required, what are the dimensions of the outside rectangle?

Let w represent the width The length of a rectangular field is 18 m longer than the width. The field is enclosed with fencing and divided into two parts with a fence parallel to the shorter sides. If 216 m of fencing are required, what are the dimensions of the outside rectangle?

Let w represent the width The length of a rectangular field is 18 m longer than the width. The field is enclosed with fencing and divided into two parts with a fence parallel to the shorter sides. If 216 m of fencing are required, what are the dimensions of the outside rectangle?

Let w represent the width The length of a rectangular field is 18 m longer than the width. The field is enclosed with fencing and divided into two parts with a fence parallel to the shorter sides. If 216 m of fencing are required, what are the dimensions of the outside rectangle?

Let w represent the width The length of a rectangular field is 18 m longer than the width. The field is enclosed with fencing and divided into two parts with a fence parallel to the shorter sides. If 216 m of fencing are required, what are the dimensions of the outside rectangle? FENCING = 216

Let w represent the width The length of a rectangular field is 18 m longer than the width. The field is enclosed with fencing and divided into two parts with a fence parallel to the shorter sides. If 216 m of fencing are required, what are the dimensions of the outside rectangle? FENCING = 216

Let w represent the width The length of a rectangular field is 18 m longer than the width. The field is enclosed with fencing and divided into two parts with a fence parallel to the shorter sides. If 216 m of fencing are required, what are the dimensions of the outside rectangle? FENCING = 216

Let w represent the width The length of a rectangular field is 18 m longer than the width. The field is enclosed with fencing and divided into two parts with a fence parallel to the shorter sides. If 216 m of fencing are required, what are the dimensions of the outside rectangle? FENCING = 216

Let w represent the width The length of a rectangular field is 18 m longer than the width. The field is enclosed with fencing and divided into two parts with a fence parallel to the shorter sides. If 216 m of fencing are required, what are the dimensions of the outside rectangle? FENCING = 216

Let w represent the width The length of a rectangular field is 18 m longer than the width. The field is enclosed with fencing and divided into two parts with a fence parallel to the shorter sides. If 216 m of fencing are required, what are the dimensions of the outside rectangle? FENCING = 216

Let w represent the width The length of a rectangular field is 18 m longer than the width. The field is enclosed with fencing and divided into two parts with a fence parallel to the shorter sides. If 216 m of fencing are required, what are the dimensions of the outside rectangle? FENCING = 216 216 =

Clearly shows that you are subtracting the same thing from both sides

Clearly shows that you are dividing by the same thing on both sides

Go back and read the problem

Let w represent the width The length of a rectangular field is 18 m longer than the width. The field is enclosed with fencing and divided into two parts with a fence parallel to the shorter sides. If 216 m of fencing are required, what are the dimensions of the outside rectangle?

Let w represent the width The length of a rectangular field is 18 m longer than the width. The field is enclosed with fencing and divided into two parts with a fence parallel to the shorter sides. If 216 m of fencing are required, what are the dimensions of the outside rectangle? The width = 36 m and The length = 54 m

Check if the fencing = 216 m FENCING = 216 The length of a rectangular field is 18 m longer than the width. The field is enclosed with fencing and divided into two parts with a fence parallel to the shorter sides. If 216 m of fencing are required, what are the dimensions of the outside rectangle? FENCING = 216 Click to go To List of Problems

4 Example #4

A triangle is isosceles, that is, it has two sides of equal length A triangle is isosceles, that is, it has two sides of equal length. The third side is 30 inches shorter than twice the length of each congruent side. The perimeter is 570 inches. Find the length of each side. Click to go To List of Problems

Let x represent the length of each equal side A triangle is isosceles, that is, it has two sides of equal length. The third side is 30 inches shorter than twice the length of each congruent side. The perimeter is 570 inches. Find the length of each side.

Let x represent the length of each equal side A triangle is isosceles, that is, it has two sides of equal length. The third side is 30 inches shorter than twice the length of each congruent side. The perimeter is 570 inches. Find the length of each side.

Let x represent the length of each equal side A triangle is isosceles, that is, it has two sides of equal length. The third side is 30 inches shorter than twice the length of each congruent side. The perimeter is 570 inches. Find the length of each side.

Let x represent the length of each equal side A triangle is isosceles, that is, it has two sides of equal length. The third side is 30 inches shorter than twice the length of each congruent side. The perimeter is 570 inches. Find the length of each side.

Let x represent the length of each equal side A triangle is isosceles, that is, it has two sides of equal length. The third side is 30 inches shorter than twice the length of each congruent side. The perimeter is 570 inches. Find the length of each side.

Let x represent the length of each equal side A triangle is isosceles, that is, it has two sides of equal length. The third side is 30 inches shorter than twice the length of each congruent side. The perimeter is 570 inches. Find the length of each side. Perimeter = 570

Let x represent the length of each equal side A triangle is isosceles, that is, it has two sides of equal length. The third side is 30 inches shorter than twice the length of each congruent side. The perimeter is 570 inches. Find the length of each side. Perimeter = 570

Let x represent the length of each equal side A triangle is isosceles, that is, it has two sides of equal length. The third side is 30 inches shorter than twice the length of each congruent side. The perimeter is 570 inches. Find the length of each side. Perimeter = 570

Let x represent the length of each equal side A triangle is isosceles, that is, it has two sides of equal length. The third side is 30 inches shorter than twice the length of each congruent side. The perimeter is 570 inches. Find the length of each side. Perimeter = 570

Let x represent the length of each equal side A triangle is isosceles, that is, it has two sides of equal length. The third side is 30 inches shorter than twice the length of each congruent side. The perimeter is 570 inches. Find the length of each side. Perimeter = 570

Clearly shows that you are adding the same thing to both sides

Clearly shows that you are dividing by the same thing on both sides

Go back and read the problem

Let x represent the length of each equal side A triangle is isosceles, that is, it has two sides of equal length. The third side is 30 inches shorter than twice the length of each congruent side. The perimeter is 570 inches. Find the length of each side.

Let x represent the length of each equal side A triangle is isosceles, that is, it has two sides of equal length. The third side is 30 inches shorter than twice the length of each congruent side. The perimeter is 570 inches. Find the length of each side.

Let x represent the length of each equal side A triangle is isosceles, that is, it has two sides of equal length. The third side is 30 inches shorter than twice the length of each congruent side. The perimeter is 570 inches. Find the length of each side.

Let x represent the length of each equal side A triangle is isosceles, that is, it has two sides of equal length. The third side is 30 inches shorter than twice the length of each congruent side. The perimeter is 570 inches. Find the length of each side.

Let x represent the length of each equal side A triangle is isosceles, that is, it has two sides of equal length. The third side is 30 inches shorter than twice the length of each congruent side. The perimeter is 570 inches. Find the length of each side. The equal sides = 150 in and The third side = 270 in

Check out the Perimeter A triangle is isosceles, that is, it has two sides of equal length. The third side is 30 inches shorter than twice the length of each congruent side. The perimeter is 570 inches. Find the length of each side. Perimeter = 570 Click to go To List of Problems

5 Example #5

Let x represent the length of the second side The first side of a triangle is 8 m shorter than the second side. The third side is 4 times as long as the first side. The perimeter is 26 m. Find the length of each side 1st 2nd Click to go To List of Problems

Let x represent the length of the second side The first side of a triangle is 8 m shorter than the second side. The third side is 4 times as long as the first side. The perimeter is 26 m. Find the length of each side

Let x represent the length of the second side The first side of a triangle is 8 m shorter than the second side. The third side is 4 times as long as the first side. The perimeter is 26 m. Find the length of each side Perimeter = 26

Let x represent the length of the second side The first side of a triangle is 8 m shorter than the second side. The third side is 4 times as long as the first side. The perimeter is 26 m. Find the length of each side Perimeter = 26

Let x represent the length of the second side The first side of a triangle is 8 m shorter than the second side. The third side is 4 times as long as the first side. The perimeter is 26 m. Find the length of each side Perimeter = 26

Let x represent the length of the second side The first side of a triangle is 8 m shorter than the second side. The third side is 4 times as long as the first side. The perimeter is 26 m. Find the length of each side Perimeter = 26

Let x represent the length of the second side The first side of a triangle is 8 m shorter than the second side. The third side is 4 times as long as the first side. The perimeter is 26 m. Find the length of each side Perimeter = 26

Clearly shows that you are adding the same thing to both sides

Clearly shows that you are dividing by the same thing on both sides

Go back and read the problem

Let x represent the length of the second side The first side of a triangle is 8 m shorter than the second side. The third side is 4 times as long as the first side. The perimeter is 26 m. Find the length of each side

Let x represent the length of the second side The first side of a triangle is 8 m shorter than the second side. The third side is 4 times as long as the first side. The perimeter is 26 m. Find the length of each side

Let x represent the length of the second side The first side of a triangle is 8 m shorter than the second side. The third side is 4 times as long as the first side. The perimeter is 26 m. Find the length of each side

Let x represent the length of the second side The first side of a triangle is 8 m shorter than the second side. The third side is 4 times as long as the first side. The perimeter is 26 m. Find the length of each side

Let x represent the length of the second side The first side of a triangle is 8 m shorter than the second side. The third side is 4 times as long as the first side. The perimeter is 26 m. Find the length of each side

Let x represent the length of the second side The first side of a triangle is 8 m shorter than the second side. The third side is 4 times as long as the first side. The perimeter is 26 m. Find the length of each side The second side = 11 m and The first side = 3 m The third side = 12 m

Check out the Perimeter The first side of a triangle is 8 m shorter than the second side. The third side is 4 times as long as the first side. The perimeter is 26 m. Find the length of each side Perimeter = 26 26 Click to go To List of Problems