Question

in rectangle wxyz, wy = 4x - 15 and xz = 3x + 8. find the lengths of the diagonals of wxyz. length of diagonal:

Explanation:

Step1: Set diagonals equal (rectangle property)

In a rectangle, diagonals are congruent, so $WY = XZ$. Substitute the given expressions:
$4x - 15 = 3x + 8$

Step2: Solve for $x$

Subtract $3x$ from both sides, then add 15 to both sides:
$4x - 3x = 8 + 15$
$x = 23$

Step3: Calculate diagonal length

Substitute $x=23$ into $XZ = 3x + 8$:
$3(23) + 8 = 69 + 8 = 77$
(Verify with $WY = 4(23)-15=92-15=77$, same result)

Answer:

77