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Math Help - Find Length and Width of Rectangle

  1. #1
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    Find Length and Width of Rectangle

    If the perimeter of a rectangle is 20 feet and the diagonal is 2 (sqrt{13}) feet, then what are the length and width?
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  2. #2
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    if length = x ft and breadth = y ft

    then by given condition 2(x+y) = 20 .....(1)
    and x^2 + y^2 = (2sqr(13))^2 = 52 .....(2)
    from eq(1) x+y = 10........(3)
    from eq (2) & eq(3)
    2xy=(x+y)^2 -(x62+y^2) = 100-52 = 48


    now (x-y)^2 = x^2+y^2 - 2xy =52 - 48 =4
    or x-y =2 .......(4)

    solving (3) & (4) we get

    length (x) =6 ft
    breadth (y) = 4 ft
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  3. #3
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    much better.....

    Quote Originally Posted by ips_math View Post
    if length = x ft and breadth = y ft

    then by given condition 2(x+y) = 20 .....(1)
    and x^2 + y^2 = (2sqr(13))^2 = 52 .....(2)
    from eq(1) x+y = 10........(3)
    from eq (2) & eq(3)
    2xy=(x+y)^2 -(x62+y^2) = 100-52 = 48


    now (x-y)^2 = x^2+y^2 - 2xy =52 - 48 =4
    or x-y =2 .......(4)

    solving (3) & (4) we get

    length (x) =6 ft
    breadth (y) = 4 ft

    Much better reply.

    Thanks
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