## Elementary Algebra

Published by Cengage Learning

# Chapter 3 - Equations and Problem Solving - 3.5 - Problem Solving - Problem Set 3.5 - Page 130: 9

#### Answer

The first side is 6 cm. The second side is 19 cm. The third side is 21 cm.

#### Work Step by Step

Let X represent the first side. The second side is 1 centimeter longer than three times the first side, which equals 3X + 1. The third side is 2 centimeters longer than the second side. Since the second side is 3X + 1, the third side equals 3X + 1 + 2 = 3X + 3. The perimeter of a triangle is equal to the sum of all its sides. Since the perimeter of the triangle is 46, we can set up the following equation: X + 3X + 1 + 3X + 3 = 46 7X + 4 = 46 Subtract 4 from both sides. 7X = 42 Divide both sides by 7. X = 6 The first side is 6. The second side is 3 $\times$ 6 + 1 = 19. The third side is 3 $\times$ 6 + 3 = 21.

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