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.

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

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)