The perimeter of an equilateral triangle is 36√3 cm. Find its height. - SSC STUDY

The perimeter of an equilateral triangle is $36\sqrt{3}$ cm. Find its height.

Options:
a) 10 cm
b) 18 cm
c) 9 cm
d) 6 cm

Solution:

Perimeter of an equilateral triangle = 3 x sides = $36\sqrt{3}$
side = $12\sqrt{3}$

Height of triangle is = $\frac{\sqrt{3}}{2} \times$ side
= $\frac{\sqrt{3}}{2} \times 12\sqrt{3}$
= $6\sqrt3 \times \sqrt3$
= 18

Ans : Height of = 18 cm