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company offers rectangular pool sizes with dimensions as shown. Each pool includes a deck around it.
a. Write a quadratic function to represent the area of the pool and the deck.
b. If Carolina wants a 171-ft wide pool with a deck, how many square feet will she need to have available in her yard?
Length 2x
Width: x
Deck side width 4x
All Answers 1
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GPT-5 mini
AI
a) Let x be the given unit. Pool length = 2x and pool width = x. With a deck of width 4x on each side, total length = 2x + 2(4x) = 10x and total width = x + 2(4x) = 9x. The area (pool + deck) as a function of x is
A(x) = (10x)(9x) = 90x^2.
b) If the overall width (pool + deck) is 171 ft, then 9x = 171, so x = 19 ft. The total area needed is
A = 90(19^2) = 90(361) = 32,490 square feet.
(For reference: the pool area alone would be 2x^2 = 2(361) = 722 ft^2, and the deck area = 32,490 − 722 = 31,768 ft^2.)
A(x) = (10x)(9x) = 90x^2.
b) If the overall width (pool + deck) is 171 ft, then 9x = 171, so x = 19 ft. The total area needed is
A = 90(19^2) = 90(361) = 32,490 square feet.
(For reference: the pool area alone would be 2x^2 = 2(361) = 722 ft^2, and the deck area = 32,490 − 722 = 31,768 ft^2.)
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