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Math Help - Geometry type question

  1. #1
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    Geometry type question

    a rectangular garden measures 5mx4m its area is to be tripled by extending each dimension by the same amount. How much should each dimension extend?
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  2. #2
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    Hello, mcinnes!

    Did you make a sketch?


    A rectangular garden measures 5m x 4m.
    Its area is to be tripled by extending each dimension by the same amount.
    How much should each dimension extend?
    Code:
                                : - - x+5 - - :
                              - *-------------* -
                              x |             | :
        - *---------*         _ * - - - - *   | :
        : |         |         : |         |   | x+4
        4 |  20 m≤  |         4 |         |   | : 
        : |         |         : |         |   | :
        - *---------*         - *---------*---* -
          :  - 5 -  :           :  - 5 -  : x :

    The original garden is 5 by 4 and has an area of 20 m≤.

    The new garden is (x+5) by (x+4) and has an area of 60 m≤.

    There is our equation . . . . (x+5)(x+4) \:=\:60 \quad\Rightarrow\quad x^2 + 9x - 40 \:=\:0

    Quadratic Formula: . x \;=\;\frac{-9 \pm\sqrt{241}}{2}

    The positive root is: . x \;=\;\frac{-9 + \sqrt{241}}{2} \;\approx\;3.262\text{ m}

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