The perimeter of an equilateral triangle is 36$$\sqrt3$$​ m. Find the height (in metres).

Correct option is D

Given:

Perimeter of equilateral triangle = $$36\sqrt{3}$$​ m

Formula Used:

Side of equilateral triangle = $$\frac{\text{Perimeter}}{3}$$​​

Height h of an equilateral triangle of side a: h = $$\frac{\sqrt{3}}{2} \times a$$​​

Solution:

Side of equilateral triangle  = $$\frac{36\sqrt{3}}{3} = 12\sqrt{3} m$$​​

Now,

Height, h = $$\frac{\sqrt{3}}{2} \times 12\sqrt{3}$$ 

$$= \frac{12 \times 3}{2} = \frac{36}{2} = 18 \text{ m}$$​​