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Math Help - Area reduction problem

  1. #1
    ronheid
    Guest

    Area reduction problem

    I have a rectangle which consists of a width of 10", and a length of 40". THis gives me a total area of 400" (w x l= a). If I reduce the area by a percentage, lets say 10% my reduced area is now 360" (400 - 40 = 360.) What is the formula to determine the reduced size of the width and the length.

    W = 10"
    L = 40"
    A = 400

    reduced rectangle 10% of area
    A2 = 360
    W2 = ?
    L2 = ?

    Thanks for your help.
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  2. #2
    hpe
    hpe is offline
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    Joined
    Apr 2005
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    Quote Originally Posted by ronheid
    I have a rectangle which consists of a width of 10", and a length of 40". THis gives me a total area of 400" (w x l= a). If I reduce the area by a percentage, lets say 10% my reduced area is now 360" (400 - 40 = 360.) What is the formula to determine the reduced size of the width and the length.

    W = 10"
    L = 40"
    A = 400

    reduced rectangle 10% of area
    A2 = 360
    W2 = ?
    L2 = ?

    Thanks for your help.
    Reduce both width and length by 5.13% (leaving 94.87%). Since 0.9487 \cdot 0.9487 \approx 0.90, this will reduce the area by 10%.

    The general formula: To reduce the area by x%, reduce the linear dimensions by 100\left(1 - \sqrt{1 - \frac{x}{100}}\right)\%.
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