Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 3 - Equations and Problem Solving - 3.5 - Problem Solving - Problem Set 3.5: 11

Answer

The length of a side of the triangle is 12 cm.

Work Step by Step

Let X represent the length of a side of the square. The length of a side of the triangle is 4 centimeters more than the length of a side of the square, which equals X + 4. The perimeter of a triangle is equal to the sum of all its sides. The perimeter of the triangle equal x + 4 + x + 4 + x + 4 = 3x + 12 The perimeter of a square equals 4 $\times$ the length of its side. The perimeter of a square equals 4 $\times$ X = 4X Since the perimeter of the triangle (3X + 12) is 4 centimeters more than the perimeter of the square (4X), we set up the following equation. 3X + 12 = 4X + 4 8 = X The length of a side of the triangle is X + 4. Since X = 8, the length of a side of the triangle is 8 + 4 = 12.
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