Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 7 - Similarity - Common Core Cumulative Standards Review - Selected Response - Page 486: 19


$x = 8$

Work Step by Step

In the rectangle described, both $\overline{AC}$ and $\overline{BD}$ are diagonals of the rectangle. According to Theorem 6-15, diagonals of a rectangle are congruent to one another. Therefore, we can set the two expressions that are given for the two diagonals equal to one another: $AC = BD$ Let's plug in our expressions for each diagonal: $5(x - 2) = 3(x + 2)$ Use the distributive property first: $5x - 10 = 3x + 6$ Add $10$ to each side of the equation to move constants to the right of the equation: $5x = 3x + 16$ Subtract $3x$ from each side: $2x = 16$ Divide each side by $2$ to solve for $x$: $x = 8$
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