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.