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Math Help - Triangle inside rectangle

  1. #1
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    Triangle inside rectangle

    Rectangle A(0,a), B(b,a), C(b,0), D(0,0).

    E is on diagonal AC, F on diagonal BD; u = AE = BF.

    G is situated below EF, forming isosceles triangle EFG;
    rectangle ABCD's center is inside triangle EFG.

    AreaABCD / areaEFG = d.

    What is the length of EG (or FG) in terms of a,b,d,u ?

    An example:
    a=84, b=112, d=49, u=55 results in isosceles triangle equal sides=20 and base = 24.
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  2. #2
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    a try

    one of EG or FG must be a side of the isosceles triangle. i'll try to solve that one, let it be s.

    we know AE = BF therefore EF is parallel to AB, using ratios, we know that
    b/s = sqrt(a^2+b^2)/abs(2u - sqrt(a^2+b^2))

    we can solve for s from there
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  3. #3
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    s = SQRT(16a^2b^2 + d^2q^4) / (2rq)
    where:
    q = SQRT(b^2(c - 2u)^2) / c
    where:
    c = SQRT(a^2 + b^2)
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