area of triangle - If the area of the equilateral triangle is 24 \sqrt{3} square cm, then find its perimeter

Krishna (last edited 4 years ago) (Expert, Educator @Qalaxia)

Step 1: Set up a area of the equilateral triangle formula.

NOTE: Equilateral triangle all sides are equal.

Area of equilateral triangle = \frac{\sqrt{3}}{4} a^2

Step 2: Use the area of equilateral triangle formula to find the side of the equilateral.

\frac{\sqrt{3}}{4} a^2 = 24 \sqrt{3}

a^2 = 24 \sqrt{3} * \frac{4}{\sqrt{3}}

a^2 = 96

a = 4 \sqrt{6}

Step 3: Calculate the perimeter of the equilateral triangle

Perimeter = a + a + a = 3 * 4 \sqrt{6}

Perimeter of the equilateral triangle = 12 \sqrt{6}