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Find the length and width of a rectangle that has the given area and a minimum perimeter. Area: 162 square feet?
2 Answers
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- The GnosticLv 72 weeks ago
Since the area is 162 feet, the dimensions of the rectangle are a length L and a width 162/L.
The perimeter is P(L) = 2L + 324/L and we want P(L) to be a minimum.
P ' (L) = 2 - 648/L². Set P ' (L) to 0 and:
648/L² = 2
648/2 = L² = 324
L = 18
162/18 = 9
The length is 7feet and the width is 18 feet.
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