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maths (mensuration)

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The area of an equilatoral triangle ABC is 50cm^2 . Find AB.

  • maths (mensuration) -

    We know all angles are 60┬░ and all sides are equal.
    Let the side be x cm

    (1/2)(x)(x)sin60┬░ = 50
    x^2 = 100/(√3/2) = 200/√3
    x = 10√2/(√√3)) = appr. 10.75 cm

    or let each side be 2x
    then the height is √3 x

    area = (1/2)(2x)(√3x) = 50
    √3x^2 = 50
    x^2 = 50/√3
    x = 5.3728 appr.
    so 2x, the side is appr. 10.75

  • maths (mensuration) -

    Area = (1/2)*base*(base/2)*sqrt3
    = (sqrt3)(base)^2/4 = 50

    base^2 = 200/sqrt3 = 115.47
    base = 10.7456599

    All sides have that length, since the triangle is equilateral.

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