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Harrizon [31]
3 years ago
8

A rectangular swimming pool is to be built with an area of 1800 square feet. The owner wants 5- foot wide decks along the two si

des and 10-foot wide decks at the two ends. Find the dimensions of the smallest piece of land on which the pool (including the decks) can be built satisfying these conditions.
Mathematics
1 answer:
tino4ka555 [31]3 years ago
3 0

Answer:  y = 20\sqrt{15}feet, x = 10\sqrt{15}feet

Step-by-step explanation:

given data:

area of the pool = 1800 square feet.

length along the deck = 5- foot

length of side along the deck = 10-foot

<u><em>Solution:</em></u>

<em>dimension of  the pool = </em>x * y<em />

<em>total area </em>A = (20+y)(10+x)<em />...................eqn1<em />

<em>since </em>xy = 3000\\<em />

<em />y = \frac{3000}{x}<em />..............................eqn2<em />

<em>insert eqn2 into eqn1</em>

<em />A = (\frac{3000}{x} +20)(10+x)<em />

<em />A = \frac{3000(x+10)}{x^{2} } + \frac{3000}{x} +20<em />

<em />20 - \frac{30000}{x^{2} } = 0<em />

<em />x = 10\sqrt{15}<em>feet</em>

<em>to solve for y, </em>\frac{60000}{x^{3} }<em />

<em />y = 20\sqrt{15}

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