Choose the correct answer of the following question:
Each side of an equilateral triangle is $6 \sqrt{3} \mathrm{~cm}$. The altitude of the triangle is
(a) $8 \mathrm{~cm}$
(b) $9 \mathrm{~cm}$
(c) $3 \sqrt{3} \mathrm{~cm}$
(d) $6 \mathrm{~cm}$
As, area of an equilateral triangle $=\frac{\sqrt{3}}{4} \times(\text { side })^{2}$
$\Rightarrow \frac{1}{2} \times$ Base $\times$ Height $=\frac{\sqrt{3}}{4} \times(6 \sqrt{3})^{2}$
$\Rightarrow \frac{1}{2} \times 6 \sqrt{3} \times$ Height $=\frac{\sqrt{3}}{4} \times 36 \times 3$
$\Rightarrow 3 \sqrt{3} \times$ Height $=27 \sqrt{3}$
$\Rightarrow$ Height $=\frac{27 \sqrt{3}}{3 \sqrt{3}}$
$\therefore$ Height $=9 \mathrm{~cm}$
Hence, the correct option is (b).
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