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Math Help - The dimensions of a garden are in whole numbers.

  1. #1
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    The dimensions of a garden are in whole numbers.

    The dimensions of a garden are in whole numbers. If the length is reduced by 3 and the width reduced 1 then the area is reduced by half. What is the are of original rectangle.
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  2. #2
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    Re: The dimensions of a garden are in whole numbers.

    Hello, alden35!

    Is some information missing?
    The problem does not have a unique solution.


    The dimensions of a garden are in whole numbers.
    If the length is reduced by 3 and the width reduced 1, the area is reduced by half.
    What is the area of original rectangle?

    Let L = the length
    and W = the width.

    We have: . (L-3)(W-1) \:=\:\tfrac{1}{2}LW

    Solve for W\!:\;W \;=\;\frac{2(L-3)}{L-6}


    Assuming that L > W, I still get two possible areas.

    . . \begin{array}{ccc} \text{Length} & \text{Width} & \text{Area} \\ \hline 8 & 5 & 40 \\ 9 & 4 & 36 \\ 12 & 3 & 36 \end{array} \qquad \begin{array}{ccc}L\!-\!3 & W\!-\!1 & \text{Area} \\ \hline 5 & 4 & 20 \\ 6 & 3 & 18 \\ 9 & 2 & 18 \end{array}
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