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23 April, 22:52

An equilateral triangle has an altitude length of 27 feet. Determined the length of a side of the triangle

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  1. 24 April, 00:25
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    Ok equilateral triangle

    altitude=27

    height=27

    if you drwa the height, you see that the equilateral triangle is split up into 2 right trnalges

    base=1/2 of one side

    hypotonuse=1 side

    vertical side=27

    represent measure of 1 side as x

    base=x/2

    hypotonuse=x

    vertical side=27

    we have a right triangle

    use pythagoran theorem

    a^2+b^2=c^2

    a=x/2

    b=27

    c=x

    so

    (x/2) ^2+27^2=x^2

    (x^2) / 4+729=x^2

    multiply both sides by 4 to clear fraction

    x^2+2916=4x^2

    subtract x^2 fromboth sides

    2916=3x^2

    divide both sides by 3

    972=x^2

    squuare root both sides

    18√3

    one side is 18√3 feet or aprox 31.1769 feet
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