## Elementary Geometry for College Students (7th Edition)

Published by Cengage

# Chapter 4 - Review Exercises - Page 217: 13

#### Answer

$AB = 17$ cm $BC = 31$ cm $CD = 17$ cm $DA = 31$ cm

#### Work Step by Step

Since $\square ABCD$ is a parallelogram, this means that $AB = CD$ and also $BC = DA$. $CD = 2x + 3$ $BC = 5x - 4$ $Perimeter = 96$ cm 1. Solve for$x$ Perimeter $= (2 \times CD) + (2 \times BC)$ $96 = 2(2x+3) + 2(5x-4)$ $96 = (4x+6) + (10x - 8)$ $96 = 14x - 2$ $98 = 14x$ $x = \frac{98}{14}$ $x = 7$ cm 2. Substitute the $x$ value into the $CD$ and $BC$ equations (Remember that $AB = CD$ and $BC = DA$) $AB = 2x + 3$ $AB = 2(7) + 3$ $AB = 14 + 3$ $AB = 17$ cm $BC = 5x - 4$ $BC = 5(7) -4$ $BC = 35 -4$ $BC = 31$ cm $CD = 2x + 3$ $CD = 2(7) + 3$ $CD = 14 + 3$ $CD= 17$ cm $DA = 5x - 4$ $DA = 5(7) -4$ $DA = 35 -4$ $DA = 31$ cm

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