Question

If the area of an equilateral triangle is 36√3 sq.cm. Find its perimeter.

Answer 1

area of equilateral triangle of side a = a²√3/4
a²√3/4 = 36√3
a² = 36*4
a = 12
perimeter of equilateral triangle = 3a = 3*12 = 36 cm.

Answer 2

Area of an Equilateral triangle = $\frac{ \sqrt{3} }{4}$ a²
a = side of each side of the triangle
Now equating,
$\frac{ \sqrt{3} }{4}$ a² = 36√3
a² = $\frac{36 \sqrt{3}* 4}{ \sqrt{3} }$ [√3 gets cancelled]
a² = 36×4
a = √6×6×2×2 = 12cm

Hence, side= 12cm

Perimeter = (Side + Side + Side)
               = (12 + 12 + 12) cm = 36 cm (answer)