Solving Problems Involving Geometry

The side of an equilateral triangle is 2” shorter than the side of a square. The perimeter of the square is 22” more than the perimeter of the triangle. Find the length of a side of the square. s t t s s t s Let t = the lengths of the sides of the triangle Let s = the lengths of the sides of the square Note: Equilateral means all sides are equal

The first equation is: t = s – 2 Now we need to find out two relationships between the lengths of the sides of the triangle and the lengths of the sides of the square. The side of the equilateral triangle is 2” shorter than the side of a square. The side of the equilateral triangle t is = 2” shorter than the side of the square s – 2 NOTE: than reverses the order. The 2 came first in English and comes last in algebra. The first equation is: t = s – 2

The second equation is: 4s = 3t + 22 We need one more relationship between the length of the sides of the triangle and the lengths of the sides of the square. The perimeter of the square is 22” more than the perimeter of the triangle. The perimeter of the square 4s is = 22” more than the perimeter of the triangle 3t + 22 NOTE: than reverses the order. The 22 came first in English and comes last in algebra. The second equation is: 4s = 3t + 22

I would solve this using substitution Now we have two equations in two unknowns: t = s – 2 4s = 3t + 22 I would solve this using substitution 4s = 3(s – 2) + 22 4s = 3s – 6 + 22 4s = 3s + 16 s = 16

Now we need to solve for t and check our work: s = 16 t = s – 2 If s = 16 and t = 14 is the second equation true? 4s = 3t + 22 4(16) = 3(14) + 22 64 = 42 + 22 64 = 64 We have a winner! The lengths of the sides of the triangle are 14 The lengths of the sides of the square are 16