Thread: 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.

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 $

Therefore, your final answers are

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


Hope this helps

Mahurshi Akilla