In equilateral triangle ABC, AB=3x and BC=2x+12. Find the numerical value of the perimeter of triangle ABC.

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  1. Since it's an equilateral triangle, AB=BC. 3x=2x+12, solve for x.

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  2. In an Equilateral triangle, all 3 sides are equal.

    Therefore AB = BC = CA
    So, 3x = 2x + 12
    Subtract 2x from both sides of the equation
    3x - 2x = 2x + 12 - 2x
    x = 12
    Therefore AB = 3x = 3 x 12 = 36
    Perimeter = AB + BC + CA = 3AB = 3 x 36 = 108

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