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Math Help - Altitude of a triangle?

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    Altitude of a triangle?

    The altitude of an equilateral triangle is 5 cm. Find the length of a side
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    Quote Originally Posted by captaintoast87 View Post
    The altitude of an equilateral triangle is 5 cm. Find the length of a side
    Let "a" be the side of an equilateral triangle.

    altitude will fall on the midpoint of opp. side

    Hence This makes a right triangle with "a/2" as base "a" as hypotnuse
    and altitude as height

    So using Pythagoras Theorem

    a^2 = a^2/4 + (altitude)^2

    Thus

    3a^2/4 = (Altitude)^2

    Hence

    Altitude = \pm \sqrt{\frac{3a}{4}}

    -ve value for length is inappropriate So the answer is tell me incase you can't digest this cake
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