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  1. #1
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    triangle

    A right triangle has a side length of 21 inches and a hypotenuse of 29 inches. A second triangle is similar to the first and has a hypotenuse of 87 inches. what is the length of the shortest side of the second triangle?
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by xsriel View Post
    A right triangle has a side length of 21 inches and a hypotenuse of 29 inches. A second triangle is similar to the first and has a hypotenuse of 87 inches. what is the length of the shortest side of the second triangle?
    Set up a proportion to match up corresponding sides. But first we need to find the third side of your first triangle.

    c^2=a^2+b^2

    29^2=21^2+b^2

    b^2=29^2-21^2

    b=\sqrt{29^2-21^2}

    x=20 This is the shortest side of the smaller triangle

    Now set up the proportion: Smaller triangle to larger triangle:

    \frac{29}{87}=\frac{20}{y}

    Solve the proportion and you have the shorter side of the larger triangle.
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  3. #3
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    Hello, xsriel!

    This doesn't require any fancy math . . .


    A right triangle has a side of 21 inches and a hypotenuse of 29 inches.
    A second triangle is similar to the first and has a hypotenuse of 87 inches.
    What is the length of the shortest side of the second triangle?

    Using Pythagorus, a^2+b^2 \:=\:c^2, we have: . a^2 + 21^2 \:=\:29^2

    . . a^2 + 441 \:=\:841\quad\Rightarrow\quad a^2 \:=\:400\quad\Rightarrow\quad a = 20

    The first right triangle has side of 20, 21, 29.
    It looks like this:
    Code:
                      *
             29    *  *
                *     * 20
             *        *
          *  *  *  *  *
                21

    The second right triangle is similar to the first
    . . and has a hypotenuse of 87.
    It looks like this:
    Code:
                                  *
                               *  *
                            *     *
                   87    *        *
                      *           *
                   *              *
                *                 *
             *                    *
          *  *  *  *  *  *  *  *  *
    The hypotenuse is three times as large.
    . . So the entire triangle is three times as large.

    Got it?

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