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5 October, 06:51

Suppose you want to draw a rectangle where the width is 7 inches less than the length and the diagonal is 2 inches longer than the length. what are the dimensions of the rectangle?

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  1. 5 October, 07:20
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    The diagonal of a rectangle is:

    d ^ 2 = w ^ 2 + l ^ 2

    Where,

    w: width

    l: long

    Substituting values we have:

    (l + 2) ^ 2 = (l-7) ^ 2 + l ^ 2

    Rewriting we have:

    l ^ 2 + 4l + 4 = l ^ 2 - 14l + 49 + l ^ 2

    l ^ 2 - 14l + 49 - 4l - 4 = 0

    l ^ 2 - 18l + 45 = 0

    (l-15) (l-3) = 0

    The solutions are:

    l = 15

    l = 3

    The viable solution is:

    l = 15

    Thus, the width is:

    w = l-7

    w = 15-7

    w = 8

    Answer:

    the dimensions of the rectangle are:

    l = 15

    w = 8
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