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Thread: area of an equilateral triangle

  1. #1
    Senior Member Mukilab's Avatar
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    area of an equilateral triangle

    the area of an equilateral triangle is 36cm^2
    Each side is x

    Find the value of x

    I tried

    bh*1/2=36

    $\displaystyle \frac{1}{2}\frac{x}{1}\frac{72}{x}=36$

    but that just ends up cancelling everything. What do I do?

    It looks like x=1 but I'm not sure :/
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  2. #2
    MHF Contributor Unknown008's Avatar
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    $\displaystyle Area\ of\ triangle = \frac12 bh$

    $\displaystyle 36 = \frac12 bh$

    But in an equilateral triangle, $\displaystyle \frac{b\sqrt{3}}{2} = h$ (from pythagoras' theorem)

    Sub in your formula:

    $\displaystyle 36 = \frac12 b(\frac{b\sqrt{3}}{2})$

    You should be able to solve for the length of the base now.
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  3. #3
    Senior Member Mukilab's Avatar
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    nope :/

    $\displaystyle 36=\frac{72x}{2x}(\frac{x\sqrt{3}}{2})$

    $\displaystyle 36=\frac{72x^2+72x\sqrt{3}}{4x}$

    ???
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  4. #4
    MHF Contributor Unknown008's Avatar
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    Come on, it's not difficult.

    $\displaystyle 36 = \frac12 b(\frac{b\sqrt{3}}{2})$

    $\displaystyle 36 \times 2 \times 2 = b \times b \times \sqrt{3}$

    $\displaystyle b^2 = \frac{144}{\sqrt{3}}$

    Then take square root on both sides to get the length of the base, which is also equal to x.
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