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Math Help - Setting Up Equation

  1. #1
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    Setting Up Equation

    I'm having trouble setting up an equation for this question, and would appreciate any help! I think I'll be okay once I have an equation, but I can't even get it started

    A, B, C and D are posts on the banks of a 20m wide canal. A and B are 1m apart.
    If OA is the same length as CD, find how far C and D are apart.
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  2. #2
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    Hello, technology!


    A, B, C, D\text{ are posts on the banks of a 20m wide canal. }\;AB = 1

    \text{If }OA = CD\text{, find }CD.
    Code:
                x
        C o---------o D
           \        |
            \       |20
             \   1  |
            B o-----o A
               \    |
                \   |
                 \  |x
                  \ |
                   \|
                    o
                    O


    Let: . x = OA = CD.


    Note that: . \Delta OAB \sim \Delta ODC

    So we have: . \dfrac{x}{1} \:=\:\dfrac{x+20}{x} \quad\Rightarrow\quad x^2 - x - 20 \:=\:0

    . . (x-5)(x+4) \:=\:0 \quad\Rightarrow\quad x \:=\:5,\:-4


    Therefore: . x \:=\:CD \:=\:5
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  3. #3
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    Sorry for the late reply Soroban, but thanks for your help! It seems so easy now that you've explained it
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