I don't have time for a more complete solution, but this should be enough to follow:
DG=x
DC=x+1
DE=sqrt(x^2+g^2)
There are many similar triangles in the figure. Use many of them to establish:
BF=g/x
BC=g(1+x)/x
AD=(x^2+g^2)/g
Since AD=BC
x=g^(2/3)
A final proportion gives
d=BD=(g^(2/3)+1)^(3/2)

Posted by Jer
on 20161102 14:26:28 