Question

Find the perimeter of an equilateral triangle, whose area is
$16 \sqrt{3 }$
​

Answer 1

Given area of the equilateral triangle = 16√3 unit²

here we've to find the perimeter of the equilateral triangle. so first of all, we needa find the side of the triangle.

we know the formula for the area of an equilateral triangle that is √3a²/4

where a is the side of the triangle.

therefore √3a²/4 = 16√3 units²

➡ √3 a² = 16√3 × 4

➡ a² = 64√3/√3

➡ a² = 64

➡ a = √64

➡ a = 8 units

the side of the equilateral triangle is 8 units.

we also know that an equilateral triangle has 3 equal sides.

➡ side × 3 = perimeter of an equilateral triangle

it's perimeter = 8 × 3

= 24 units

hence, the perimeter of the equilateral triangle is 24 units.