geometry

the lenght of a rectangleis 6 inches more than its width. The area of the rectangle is 91 square inches. Find the dimensions of the rectangle

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  1. length is 13 inches
    width is 7 inches
    let width and length both be x;
    (x+6) [this is length] & (x) [this is width];
    (x+6) * x = 91;
    x^2+6x = 91;
    x^2 + 6x - 91 = 0;
    solve by factoring;
    (x-7)(x+13)= 0
    x = 7 & x = -13 (-13 is not real)
    check;
    L=(7+6)
    W= 7
    (7+6)*7=91

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  2. Width = W.
    Length = W+6.

    A = L*W = (W+6)W = W^2+6W = 91.
    W^2+6W-91 = 0. -91 = -7*13. sum = -7+13 = 6 = B.
    (W-7)(W+13) = 0
    W = 7 and -13.
    w = 7 in.
    L = W+6 = 7+6 = 13 in.

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