1. Solve for unknown measures
EXAMPLE 2
Solve for unknown measures
Algebra The base of a triangle is twice its height. The area of the triangle is 36 square inches. Find the base and height.
Let h represent the height of the triangle. Then the base is 2h.
A = bh 2 1
Write formula.
36 = (2h)(h) 2 1
Substitute 36 for A and 2h for b.
36 = h2
Simplify.
6 = h
Find positive square root of each side.
The height of the triangle is 6 inches, and the base is = 12 inches.
ANSWER

2. EXAMPLE 3
Solve a multi-step problem
Painting
You need to buy paint so that you can paint the side of a barn. A gallon of paint covers 350 square feet. How many gallons should you buy?
SOLUTION
You can use a right triangle and a rectangle to approximate the area of the side of the barn.

3. (338 ) EXAMPLE 3 Solve a multi-step problem STEP 1
Find the length x of each leg of the triangle.
262 = x2 + x2
Use Pythagorean Theorem.
676 = 2x2
Simplify.
338 = x
Solve for the positive value of x.
STEP 2
Find the approximate area of the side of the barn.
Area = Area of rectangle + Area of triangle
= 26(18) + 1 2
(338 )
= 637 ft2

4. Solve a multi-step problem
EXAMPLE 3
Solve a multi-step problem
STEP 3
Determine how many gallons of paint you need.
637 ft  1.82 gal
350 ft2
1 gal
Use unit analysis.
Round up so you will have enough paint. You need to buy 2 gallons of paint.

5. Let the length of the base be x
GUIDED PRACTICE
for Examples 2 and 3
A parallelogram has an area of 153 square inches and a height of 17 inches. What is the length of the base? 4.
SOLUTION
Let the length of the base be x
A = b h
Write formula.
153 = x 17
Substitute 153 for A and 17 for h and x for b.
x = 9
Simplify.
ANSWER
Length of the base is 9 in.

6. Find the length x of each leg of the triangle.
GUIDED PRACTICE
for Examples 2 and 3
WHAT IF? In Example 3, suppose there is a 5 foot by 10 foot rectangular window on the side of the barn. What is the approximate area you need to paint? 5.
SOLUTION
You can use a right triangle and a rectangle to approximate the area of the side of the barn.
STEP 1
Find the length x of each leg of the triangle.
262 = x2 + x2
Use Pythagorean Theorem.
676 = 2x2
Simplify.
338 = x
Solve for the positive value of x.

7. (338 ) GUIDED PRACTICE for Examples 2 and 3 STEP 2
Find the approximate area of the side of the barn.
Area = Area of rectangle + Area of triangle 2
(338 )
= 26(18) + 1
= 637 ft2
STEP 3
Find the area of window.
A = l b
Write formula. =
Substitute.
= 50 ft2
Multiply.

8. GUIDED PRACTICE
for Examples 2 and 3
Find the approximate area you need to paint.
STEP 4
Area of side of barn – Area of window
= 637 – 50
= 587
ANSWER
You need to paint an approximate area of 587 ft2.