# What will the dimensions of the resulting cardboard box be if the company wants to maximize the volume and they start with a flat piece of square cardboard 20 feet per side, and then cut smaller squares out of each corner and fold up the sides to create the box?

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To maximize the volume of the resulting cardboard box, the dimensions of the box will be such that the squares cut out of each corner have equal side lengths. Let's denote this side length as ( x ) feet.

Given that the original square cardboard has side length of 20 feet, after cutting squares of side length ( x ) feet from each corner, the dimensions of the resulting box will be ( (20 - 2x) ) feet by ( (20 - 2x) ) feet by ( x ) feet.

Therefore, the dimensions of the resulting cardboard box will be ( (20 - 2x) ) feet by ( (20 - 2x) ) feet by ( x ) feet.

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