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Math Help - word problem 2 (rectangular)

  1. #1
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    word problem 2 (rectangular)

    i have another question on this topic.

    a rectangular building is to have an area of 1800 sq. meters. on each side of the building there must be a walkway of 5 meters and on each end a walkway of 10 meters. What is the dimensions of the smallest rectangular piece of land that can accommodate the building?

    so, i tried
    area = xy
    = (x-5)(x-10)
    1800 = (x-5)(x-10)
    = x^2 - 15x +50
    0 = x^2 - 15x - 1750

    doesn't seem to be im doing correctly...
    what should i do?
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  2. #2
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    Quote Originally Posted by haebinpark View Post
    i have another question on this topic.

    a rectangular building is to have an area of 1800 sq. meters. on each side of the building there must be a walkway of 5 meters and on each end a walkway of 10 meters. What is the dimensions of the smallest rectangular piece of land that can accommodate the building?

    so, i tried
    area = xy
    = (x-5)(x-10)
    1800 = (x-5)(x-10)
    = x^2 - 15x +50
    0 = x^2 - 15x - 1750

    doesn't seem to be im doing correctly...
    what should i do?
    let L = building length
    W = building width

    LW = 1800

    land area = A ...

    A = (L+20)(W+10)

    use the first equation to solve for L in terms of W (or W in terms of L ... it doesn't make a difference) and substitute into the second equation to area in terms of a single variable.

    take the derivative and minimize.
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  3. #3
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    umm.. on A = (L+20)(W+10), here,
    why L+20...?
    where is 20 come from?
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  4. #4
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    Quote Originally Posted by haebinpark View Post
    umm.. on A = (L+20)(W+10), here,
    why L+20...?
    where is 20 come from?
    10 meters of walkway on each side
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