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