Question

the diagonals of a rectangle wxyz are wy = 3x + 7 and xz = 5x - 9. what is the length of each diagonal?
a 31
b. 16
c. 8
d. 24

Explanation:

Step1: Recall rectangle diagonal property

In a rectangle, diagonals are equal. So \( WY = XZ \).

Step2: Set up equation

Given \( WY = 3x + 7 \) and \( XZ = 5x - 9 \), set them equal: \( 3x + 7 = 5x - 9 \).

Step3: Solve for x

Subtract \( 3x \) from both sides: \( 7 = 2x - 9 \).
Add 9 to both sides: \( 16 = 2x \).
Divide by 2: \( x = 8 \).

Step4: Find diagonal length

Substitute \( x = 8 \) into \( WY = 3x + 7 \): \( 3(8) + 7 = 24 + 7 = 31 \)? Wait, no, wait—wait, maybe I made a mistake. Wait, no, let's check again. Wait, \( XZ = 5x - 9 \), so \( 5(8) - 9 = 40 - 9 = 31 \). Wait, but the options are 31, 16, 8, 24. Wait, but let's re - check the equation. \( 3x + 7 = 5x - 9 \). So \( 7 + 9 = 5x - 3x \), \( 16 = 2x \), \( x = 8 \). Then \( WY = 3(8)+7 = 31 \), \( XZ = 5(8)-9 = 31 \). So the length of each diagonal is 31.

Answer:

A. 31