# Thread: 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

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

$\displaystyle (x - 2)^2 = x$

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

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

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

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

$\displaystyle x = 1 , x = 4$

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

Therefore, $\displaystyle x = 4$

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

$\displaystyle x = 4, diagonal_1 = diagonal_2 = 2$