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Math Help - word problem

  1. #1
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    word problem

    if the length and the width of a rectangle are increased by two inches, the area of the rectangle is 120 square inches. if the length and the width of a rectangle are decreased by two inches, the area of the rectangle is 48 square inches. find the length of the rectangle.
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  2. #2
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    Hello, mojojojo!

    If the length and the width of a rectangle are increased by two inches,
    the area of the rectangle is 120 square inches.
    If the length and the width of a rectangle are decreased by two inches,
    the area of the rectangle is 48 square inches.
    Find the length of the rectangle.

    Let L = length of the rectangle.
    Let W = width of the rectangle.

    Then we have: . \begin{array}{ccccc}(L+2)(W+2) &=& 120 & [1] \\<br />
(L-2)(W-2) &=& 48 & [2]\end{array}

    \begin{array}{cccccc}<br />
\text{From [1] we have:} & LW + 2L + 2W + 4 &=& 120 \\<br />
\text{From [2] we have:} & LW - 2L - 2W + 4 &=& 48 \end{array}

    . . Subtract: . 4L + 4W \:=\:72 \quad\Rightarrow\quad W \:=\:18-L


    Substitute into [1]: . (L+2)(20-L) \:=\:120 \quad\Rightarrow\quad L^2 - 18L + 80 \:=\:0

    . . (L-10)(L-8) \:=\:0 \quad\Rightarrow\quad L \;=\;10,\:8


    Assuming L > W we have: . L \:=\:10\text{ inches.}

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