A rectangular swimming pool is to be built with the area of the pool being 2200

Question

A rectangular swimming pool is to be built with the area of the pool being 2200 square feet. In addition, the owner wants 5 foot wide decks along sides of the pool and 8 foot wide decks at the two ends. Determine the dimensions (to the nearest tenth of a foot) of the pool that allows the pool and decks to be built on the smallest possible piece of property. Then find the minimum area of the property used to build the pool and decks. Find the dimensions of the pool and the property (including decks). Must be solved without using derivatives.

Explanation / Answer

let the dimensions be L and B

L*B = 2200

for minimum area... total lenght = toatal width...

L+5 = B+8

L= B+3

so B(B+3) = 2200

B^2 + 3B = 2200

B = 45.918 feet

L = 48.918 feet

dimensions of pool ae 48.918 ft and 45.918 ft

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