Question

$\text{The area of an equilateral triangle is}36\sqrt{3}c{m}^2.\text{Its perimeter is}\left(a\right)36cm\left(b\right)12\sqrt{3}cm\left(c\right)24cm\left(d\right)30cm$

Answer 1

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

Hence, side= 12cm

Perimeter = (Side + Side + Side)
= (12 + 12 + 12) cm = 36 cm
option a is correct