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Math Help - Symmetry

  1. #1
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    Symmetry

    AD, EF and BD are perpendicular to AB.

    AD = 3 and BC = 5

    What is the length h?
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  2. #2
    Senior Member OReilly's Avatar
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    Quote Originally Posted by Natasha1
    AD, EF and BD are perpendicular to AB.

    AD = 3 and BC = 5

    What is the length h?
    You mean probably that AD,EF and BC are perpendicular to AB?
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by Natasha1
    AD, EF and BD are perpendicular to AB.

    AD = 3 and BC = 5

    What is the length h?
    As triangles ABD and DBF are similar:

    <br />
\frac{h}{3}=\frac{DB}{AB}\ \ \ \dots (1)<br />

    Also trianglea ABC and ADF are similar:

    <br />
\frac{h}{5}=\frac{AB-DB}{AB}<br />

    So dividing these:

    <br />
\frac{5}{3}=\frac{DB}{AB}\ \frac{AB}{AB-DB}=\frac{DB}{AB-DB}<br />

    Hence:

    <br />
DB=\frac{5}{8}AB<br />

    Substituting this into (1) then gives:

    <br />
\frac{h}{3}=\frac{5}{8}<br />
,

    or:

    <br />
h=\frac{3\times 5}{8}=\frac{15}{8}<br />

    RonL
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