Geometry - Rectangle HELP

8thmimi · Sep 4th 2007, 04:42 PM

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.

**mahurshi** · Sep 4th 2007, 05:43 PM

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( $4$ ) $= 2$

Therefore, your final answers are

$x = 4, diagonal_1 = diagonal_2 = 2$

Hope this helps

Mahurshi Akilla

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Geometry - Rectangle HELP

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