The strength, S, of a wooden beam depends on the width and depth of the rectangu

Question

The strength, S, of a wooden beam depends on the width and depth of the rectangular cross-section of the beam, but not on the length of the beam. For a particular type of wood, the value of S of a beam is proportional to the product of the width and the square of the depth of its cross-section. If the strength of an oak beam 17 inches wide and 11 inches deep is 207, determine the strength, S, to three significant figures of the strongest rectangular beam that can be cut from a 14-inch-diameter oak tree.

Explanation / Answer

You would probably want to optimize your equation for the S value. Assuming the tree is cylindrical, the beam with the greatest strength would be a square beam with side length 11/sqrt(2).

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