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# A pool 4m x 8m is surrounded by a concrete deck of uniform width. Determine the width of the deck if the total area of concrete is 50m^2?

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- stanschimLv 71 month agoFavorite Answer
Area Of Big Rectangle - Area of Small Rectangle = 50 m^2

(8 + 2x)(4 + 2x) - 8(4) = 50

32 + 16x + 8x + 4x^2 - 32 = 50

4x^2 + 24x = 50

4x^2 + 24x - 50 = 0

2(2x^2 + 12x - 25) = 0

Solve for x by using the quadratic formula. Throw out extraneous negative answer.

x = about 1.637 m

Width = 8 + 2x = 8 + 2(1.637) = about 11.274 m

- SlowfingerLv 61 month ago
Answer: w= sqrt(43/2) - 3 = 1.637m

Area is outer rectangle minus inner rectangle.

A = (4 + 2w)(8 + 2w) - 4*8 = 50

(4 + 2w)(8 + 2w) = 50 + 32 = 82

4 w^2 + 24 w - 50 = 0

w^2 + 6 w - 12.5 = 0

solve for w.

Solutions

w1 = -3 - sqrt(43/2)

w2 = -3 + sqrt(43/2)

we know w>0 so

w = w2 = -3 + sqrt(43/2) = 1.637 m

check

8+2*1.637 = 11.274

4+2*1.637 = 7.274

A = 11.274 * 7.274 - 4 * 8 = 50 m^2 ... ok.

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