Question

The surface area of a rectangular prism is 174 square inches. The rectangular base has one side length 3 times the other. The height of the prism is 5 inches. What are the maximum lengths of the sides of the base?

Answer 1

The maximum lengths of the sides of the rectangular base are approximately 7.616 inches and 22.847 inches.

How to find the maximum lengths of the sides of the base

The surface area of the rectangular prism ($A_{s}$) is equal to the product of two lengths of triangle. The area formula for the base is:

$A = x\cdot (3\cdot x)$

$A = 3\cdot x^{2}$

If we know that $A = 174$, then the least length of the base of the rectangle is:

$x = \sqrt{\frac{A}{3} }$

$x \approx 7.616\,in$

The maximum lengths of the sides of the rectangular base are approximately 7.616 inches and 22.847 inches. $\blacksquare$

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