algebra

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Find the length of a side of an equilateral triangle with altitude of length 6.

  • algebra -

    let each side of the triangle be 2x units

    then x^2 + 6^2 = (2x^2)
    x^2 + 36 = 4x^2
    3x^2 = 36
    x^2 = 12
    x = 2√3
    2x = 4√3

    or
    knowing the ratio of sides of a 30-60-90 triangle
    is 1:√3:2
    h/2 = 6/√3
    √3h=12
    h = 12/√3
    = 12/√3(√3/√3) = 12√3/3 = 4√3

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