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Rectangle Riddle

Challenger

Rectangle Riddle A

We define rectangle ABCD with diagonals AC and BD. |AM|, |AB|, and |AD| are integers. Give the area of the smallest rectangle that meets these conditions. Attention: the figure is not drawn to scale.

Mastermind

Rectangle Riddle B

We define rectangle ABCD. Somewhere on AB lies point E. Somewhere on DE lies point F such that angle DFC = 90 degrees. The triangles AED, CDF, CEF, and BCE all only have integer sides. Give the area of the smallest rectangle that meets these conditions. Attention: the figure is not drawn to scale.