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Math Help - [SOLVED] what is the answer to this problem

  1. #1
    dearlybelovedx3
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    [SOLVED] what is the answer to this problem

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  2. #2
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    Hello, dearlybelovedx3!

    In right triangle ABC, BD is the altitude to hypotenuse AC.
    AC = 20,\;BD = 6,\;AD < DC

    (a) Find AD and DC.

    (b) To the nearest tenth, find AB.
    Code:
                B
                *
               *|  *
              * |     *
             *  |6       *
            *   |           *
           *    |              *
        A * * * + * * * * * * * * * C
             x  D      20-x
          : - - - - 20  - - - - - :

    We have three similar right triangles: . \Delta ABC \sim \Delta BDC \sim \Delta ADB

    Let AD\,=\,x, then DC \,=\,20-x

    Then: . \frac{x}{6} \:=\:\frac{6}{20-x}\quad\Rightarrow\quad x^2-20x+36\:=\:0

    . . and we have: . (x-2)(x-18)\:=\:\quad\Rightarrow\quad x \:=\:2,\:18

    (a) Therefore: . AD \,=\,2,\;DC\,=\,18


    (b) In right triangle ADB, we have: . AB^2 \:=\:2^2 + 6^2 \quad\Rightarrow\quad AB \:=\:\sqrt{40}\:\approx\:6.3

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