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Thread: 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 $\displaystyle L$ = length of the rectangle.
    Let $\displaystyle W$ = width of the rectangle.

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

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

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


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

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


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

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