Let W XY Z be a square. Three parallel lines d, d’ and d” pass respectively through X, Y and Z. The distance between d and d’ is 5 and the distance between d and d” is 7. What is the area of the square ?

This problem was unusually tough after the geometry was done. The three lines gives a system of equations using Pythagorean:

2s^2 = x^2 + 44, s^2 = (x+y)^2 + 4, s^2 = y^2 + 25

But solving this system doesn’t seem to be trivial.

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