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: 8

Answer

The shortest side is 13 yards The longest side is 26 yards The third side is 15 yards

Work Step by Step

Let X represent the shortest side. The longest side is twice the shortest side, which equals 2X. The third side is 2 longer than the shortest side, which equals 2 + X. The perimeter of a triangle is equal to the sum of all its sides. Since the perimeter of the triangle is 54, we can set up the following equation: X + 2X + 2 + X = 54 4X + 2 = 54 Subtract 2 from both sides. 4X = 52 Divide both sides by 4. X = 13 The shortest side is 13 The longest side is 2 $\times$ 13 = 26. The third side is 2 + 13 = 15.
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