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Overlapped Rectangles

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Overlapped Rectangles

Two rectangles are overlapped on a corner as shown in the image. The overlapped region is a square. The length of one rectangle is twice the length of the other, and its width is half the width of the other.

If we consider the rectangles as a single geometric figure, its outer perimeter is 768 units, and its area is 8415 square units.

The perimeter of the first rectangle is 312 units.

Find the area of the overlapped square, given that all the side measures are integers.

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Problem by BogusBoy


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