Not Uniquely Determined
Geometry
Level
3
ABCD is a rectangle , P lies on AD and Q on AB . The triangles PAQ , QBC and PCD all have the same area and BQ = 2 units . The length of AQ, is
NOT UNIQUELY DETERMINED
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1 solution
Assume that ABCD is an unit square. Then immediately we have the areas (1-x) = (1-x) = x², which leads us to the golden ratio. The "2" is just to redirect us from a simpler solution, but it doubles the golden ratio.
I should add that assuming that ABCD is a square is because ratio of areas are preserved in affine transforms.