A box with a square base is to hold a volume of 200. The bottom and top are formed by folding in flaps from all four sides so that the bottom and top consist of two layers of cardboard. Find the dimensions of the box that requires the least material. Also, find the ratio of height to side of the base.

Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter59: Areas Of Rectangles, Parallelograms, And Trapezoids
Section: Chapter Questions
Problem 79A
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A box with a square base is to hold a volume of 200. The bottom and top are formed by folding in flaps from all four sides so that the bottom and top consist of two layers of cardboard. Find the dimensions of the box that requires the least material. Also, find the ratio of height to side of the base. 

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