# Rectangle Diagonal

Pro Problems > Math > Geometry > Rectangles and Squares## Rectangle Diagonal

## Solution

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The perimeter of a field is 2240 feet. The field is split down the middle, parallel to the shorter dimension. The perimeter of each half-field is 1520 feet. What is the shorter dimension of the field?

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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.

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In the diagram shown, the blue square and the yellow rectangle share a side.

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The combined area of the two figures is 384 square units.

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