Algebra

The area of a rectangular piece of land is 280 square meters. If the length of the land was 5 meters less and the width was 1 meter more, the shape of the land would be a square.

Part A: Write an equation to find the width (x) of the land. Show the steps of your work. (5 points)

Part B: What is the width of the land in meters? Show the steps of your work. (5 points)

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  1. original width --- x
    original length --- y

    xy= 280

    y = 280/x

    new width --- x+1
    new length --- y-5
    new area
    = (x+1)(y-5)
    = (x+1)(280/x - 5)
    = 280 - 5x + 280/x - 5
    = 275 - 5x + 280/x
    = (275x - 5x^2 + 280)/x
    = -5( x^2 - 55x - 56)/x

    perfect squares in the neighbourhood of 280 are
    169 , 196 , 225 , 256 , 289, 324 ...

    So I tried values of x starting at x = 13
    Lo, and behold, when x = 14
    new area = -5(14^2 - 55(14) - 56)/14 = 225 which is a perfect square.

    so the original was 14 by 20 for an area of 280

    check:
    new width = 15
    new length = 15
    new area = 225
    YEAHHH!

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    posted by Reiny

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