Elementary Geometry for College Students (5th Edition)

Published by Brooks Cole
ISBN 10: 1439047901
ISBN 13: 978-1-43904-790-3

Chapter 4 - Review Exercises: 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
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.