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Math Help - Perimeter

  1. #1
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    Perimeter

    How would I solve this?

    "The perimeter of a rectangle is 40 cm. If the length were doubled and the width halved, the perimeter would be increased by 16cm. Find the dimensions of the original rectangle."
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  2. #2
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    Quote Originally Posted by largebabies View Post
    How would I solve this?

    "The perimeter of a rectangle is 40 cm. If the length were doubled and the width halved, the perimeter would be increased by 16cm. Find the dimensions of the original rectangle."
    Let l denote the length of the rectangle and w the width. The you know:

    2l + 2w = 40
    2\cdot (2l)+2\cdot \left(\frac12w\right) = 40+16

    That means you have to solve for l and w:

    l+w=20
    4l+w=56

    I've got l = 12 and w = 8
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  3. #3
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     P=2l+2w, where l = length and w = width
    40cm=2l+2w
    and
    56cm=2*2l+\frac{2w}{2}

    56cm=4l+w

    40cm-2w=2l

    20cm-w=l

    56cm=4(20cm-w)+w

    56cm=80cm-4w+w

    -24cm=-3w

    w=8cm

    now plug w=8cm into the original equation

    40cm=2(8cm)+2w

    24cm=2w

    w=12cm
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