The area of an equilateral triangle is
Question:

The area of an equilateral triangle is $81 \sqrt{3} \mathrm{~cm}^{2}$. Its height is

(a) $9 \sqrt{3} \mathrm{~cm}$

(b) $6 \sqrt{3} \mathrm{~cm}$

(c) $18 \sqrt{3} \mathrm{~cm}$

(d) 9 cm

Solution:

(a) $9 \sqrt{3} \mathrm{~cm}$

Area of equilateral triangle $=81 \sqrt{3} \mathrm{~cm}^{2}$

$\Rightarrow \frac{\sqrt{3}}{4} \times(\text { Side })^{2}=81 \sqrt{3}$

$\Rightarrow(\text { Side })^{2}=81 \times 4$

$\Rightarrow(\text { Side })^{2}=324$

$\Rightarrow$ Side $=18 \mathrm{~cm}$

Now,

Height $=\frac{\sqrt{3}}{2} \times$ Side $=\frac{\sqrt{3}}{2} \times 18=9 \sqrt{3} \mathrm{~cm}$