Geometry: Common Core (15th Edition)

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

Chapter 6 - Polygons and Quadrilaterals - 6-4 Properties of Rhombuses, Rectangles, and Squares - Practice and Problem-Solving Exercises - Page 380: 19


$x = 3$

Work Step by Step

According to Theorem 6-15, the diagonals of a rectangle are congruent. Therefore, we can set $LN$ and $MP$, the diagonals of $LMNP$, equal to one another to solve for $x$: $LN = MP$ Substitute with the expressions given for each diagonal: $5x - 8 = 2x + 1$ Subtract $2x$ from each side of the equation to move variables to the left side of the equation: $3x - 8 = 1$ Add $8$ to each side of the equation to move constants to the right side of the equation: $3x = 9$ Divide each side by $3$ to solve for $x$: $x = 3$
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