## Geometry: Common Core (15th Edition)

Published by Prentice Hall

# Chapter 6 - Polygons and Quadrilaterals - 6-4 Properties of Rhombuses, Rectangles, and Squares - Practice and Problem-Solving Exercises - Page 380: 20

#### Answer

$x = 1$

#### 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: $3x + 1 = 8x - 4$ Subtract $8x$ from each side of the equation to move variables to the left side of the equation: $-5x + 1 = -4$ Subtract $1$ from each side of the equation to move constants to the right side of the equation: $-5x = -5$ Divide each side by $-5$ to solve for $x$: $x = 1$

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.