# Math Help - Geometry - Rectangle HELP

1. ## Geometry - Rectangle HELP

I need help with the following problem:

If rectangle WXYZ, diagonal WY = x-2 and diagonal XZ = square root of x. Find x and the length of the diagonals of WXYZ.

2. ## How to solve rectangle problems with diagonals

Originally Posted by 8thmimi
I need help with the following problem:

If rectangle WXYZ, diagonal WY = x-2 and diagonal XZ = square root of x. Find x and the length of the diagonals of WXYZ.

In a rectangle, the diagonals measure the same

$
x - 2 =$
sqrt( $x$)

$
(x - 2)^2 = x
$

$
x^2 - 4x + 4 = x
$

$
x^2 - 4x - x + 4 = 0
$

$
x(x - 4)-1(x - 4) = 0
$

$
(x - 1)(x - 4) = 0
$

$
x = 1 , x = 4
$

If $x = 1$
$diagonal_1 = x - 2 = -1$ ... this is not possible (since diagonal can't be a negative number)

Therefore, $x = 4$

$diagonal_1 = x - 2 = 4 - 2 = 2$
$diagonal_2 =$sqrt( $x$) = sqrt( $4$) $= 2$

$x = 4, diagonal_1 = diagonal_2 = 2$