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Use as much of the string as is possible to make the circle.

In the limit, the circumference of the circle is 50 inches and the perimeter of the square is 0. This gives a circle with an area of 198.94 sq inches and a square with an area of 0 sq inches. Any string moved from the circle to the square will reduce the total area.

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Q: Given a length of string L equals 50 inches construct a circle and a square such that the sum of the areas is a maximum?
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