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: 13

Answer

The shortest side equals 8 cm. The lon­gest side is 17 cm. The other side is 15 cm.

Work Step by Step

Let X represent the shortest side. The lon­gest side is 1 centimeter longer than twice the shortest side, which equals 1 + 2X. The other side is 2 centimeters shorter than the longest side. It equals 1 + 2X - 2 = 2X - 1. The perimeter of a triangle is equal to the sum of all its sides. The perimeter of a triangle is 40 centimeters, so we can set up the following equation: X + 1 + 2X + 2X - 1 = 40 5X = 40 Divide both sides by 5. X = 8 The shortest side equals 8. The lon­gest side is 1 + 2 $\times$ 8 = 1 + 16 = 17. The other side is 2 $\times$ 8- 1 = 15.
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