Anonymous
Anonymous asked in Science & MathematicsMathematics · 4 weeks ago

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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  • 4 weeks ago
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    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

  • 4 weeks 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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