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If the width of a rectangle is increased by 2 inches, the area is 140 square inches. If the legnth is increased by 1 inch, the area is 120 inches. Find the dimensions of the rectangle.

  • Math -

    From the description above, we know that:

    (W+2) x L = 140
    (L+1) x W = 120

    where W = the width and L is the length, so...

    WL + 2L = 140
    WL + W = 120

    Subtract the second equation from the first, you get...

    2L - W = 20, so
    W = 2L - 20.

    So feed that back into the first of the original two equations:

    (2L - 18) x L = 140

    2L² - 18L - 140 = 0
    so L² - 9L - 70 = 0
    factorize it: (L - 14)(L + 5) = 0

    so L = 14 or L = -5. The latter is impossible, so L = 14.
    But W = 2L - 20, so W = 8.

    Check it:

    (W+2) x L = 10 x 14 = 140 Correct.
    (L+1) x W = 15 x 8 = 120 Correct.

    Answer: W = 8; L = 14.

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