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Math Help - Geometry - Rectangle HELP

  1. #1
    8thmimi
    Guest

    Unhappy 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.
    Last edited by 8thmimi; September 4th 2007 at 07:25 PM.
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  2. #2
    Newbie
    Joined
    Sep 2007
    Posts
    20

    How to solve rectangle problems with diagonals

    Quote Originally Posted by 8thmimi View Post
    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

    <br />
x - 2 = sqrt( x)

    <br />
(x - 2)^2 = x<br />

    <br />
x^2 - 4x + 4 = x<br />

    <br />
x^2 - 4x - x + 4 = 0<br />

    <br />
x(x - 4)-1(x - 4) = 0<br />

    <br />
(x - 1)(x - 4) = 0<br />

    <br />
x = 1 , x = 4<br />


    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
    Last edited by mahurshi; September 6th 2007 at 06:40 AM. Reason: trying out tex
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