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