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A storage shed is to be built in the shape of a box with a square...

A storage shed is to be built in the shape of a box with a square base. It is to have a volume of 125 cubic feet. The concrete for the base costs ​$8 per square​ foot, the material for the roof costs $7 per square​ foot, and the material for the sides costs ​$7.50 per square foot. Find the dimensions of the most economical shed.

The length of one side of the​ shed's base is

The height of the shed is

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