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5 August, 18:45

the length of a rectangle is 7 cm less than its width what are the dimensions of the rectangle if its area is 120 cm²

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  1. 5 August, 19:03
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    Answer: The length of the rectangle is 8cm while the width is 15cm.

    Step-by-step explanation: The length of the rectangle has been described as 7cm less than it's width. This means if the width is given as W, then the length would be 7 less than W, that is, length would be W - 7. Also the area has been given as 120. With this bit of information we can now express the area as follows;

    Area of a rectangle = L x W

    Where area is 120, length is W - 7 and width is W.

    120 = (W-7) x W

    120 = W^2 - 7W

    We rearrange all terms on one side of the equation and we now have

    W^2 - 7W - 120 = 0

    What we now have is a quadratic equation, and by factorizing we now have

    (W + 8) (W - 15) = 0

    (W + 8) = 0 and (W - 15) = 0

    Hence, either W + 8 = 0 and W = - 8

    OR W - 15 = 0 and W = 15.

    We know that the dimensions of the rectangle cannot be a negative number, so we choose W = 15.

    Having calculated that, if the length is given as W - 7, then the length is

    L = 15 - 7

    L = 8

    Therefore, the length is 8cm and the width is 15cm.
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