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Math Help - perpendicular segment measure

  1. #1
    rcs
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    perpendicular segment measure

    Let ABCD be a square with each side of length 2cm. Let E be the midpoint of AB. How long is the perpendicular segment C to DE?

    can anyone help me on this please
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  2. #2
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    Re: perpendicular segment measure

    make a sketch ... use the fact that the sides of similar triangles are proportional.
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  3. #3
    rcs
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    Re: perpendicular segment measure

    is this correct 2* sqrt(5) / 5
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    Re: perpendicular segment measure

    JHello, rcs!

    Your answer is close, but . . .


    Let ABCD be a square with each side of length 2cm.
    Let E be the midpoint of AB.
    How long is the perpendicular segment from C to DE?

    Code:
                1     E
        A o - - - - - o - - - - - o B
          |        θ /            |
          |         /             |
          |      F /              |
          |    _  o               |
          |   √5 /  *             |
        2 |     /     *           |
          |    /        *         |
          |   /           *       |
          |  /              *     |
          | /                 *   |
          |/ θ                  * |
        D o - - - - - - - - - - - o C
                      2
    In right triangle EAD, the hypotenuse is: DE \,=\,\sqrt{1^2+2^2} \,=\,\sqrt{5}

    Right triangles EAD and DFC have angle \theta.
    . . Hence: . \Delta EAD \sim \Delta DFC

    \begin{array}{cccccccc}\text{In }\Delta DFC:& \sin\theta &=& \dfrac{CF}{2} \\ \\[-3mm] \text{In }\Delta EAD: & \sin\theta &=& \dfrac{2}{\sqrt{5}} \end{array}

    Therefore: . \frac{CF}{2} \:=\:\frac{2}{\sqrt{5}} \quad\Rightarrow\quad CF \:=\:\frac{4}{\sqrt{5}} \;=\;\frac{4\sqrt{5}}{5}
    Thanks from rcs
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