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Problem of the Week
Problem E
Zigzagged

A fence is to be constructed in a zigzag pattern inside a rectangular field, as shown.

Rectangle ABCD with top left vertex A, length AB, and width AD. E is on AB, H and G are on CD, with H to the left of G, and F is on BC. The fence starts at vertex A and goes from A to H to E to G to F.

The fence will be constructed so that \(\angle AHD=\angle EHG\), \(\angle AEH=\angle BEG\), \(\angle EGH=\angle FGC\), and \(CF=12\) m. If \(AB=36\) m and \(AD=20\) m, determine the total length of fencing required. That is, determine the value of \(AH + EH + EG + FG.\)