Question

If the area of an equilateral triangle is $9\sqrt{3}{cm}^2$. What is the length of the side of the triangle.

• A. 8 cm
• B. 9 cm
• C. 18 cm
• D. 6 cm

Answer 1

The correct option is D

6 cm

Let the side of the equilateral triangle = a cm.

Semi Perimeter, s = $\frac{3a}{2}$

$s-a=\frac{3a}{2}-a=\frac{3a-2a}{2}=\frac{a}{2}$

Now by heron’s formula

Area of the triangle= $\sqrt{s(s-a)(s-b)(s-c)}$

$\Rightarrow 9\sqrt{3}=\sqrt{\frac{3a}{2}\times \frac{a}{2}\times \frac{a}{2}\times \frac{a}{2}}$

$\Rightarrow \sqrt{243}=\sqrt{\frac{3a^4}{16}}$

Squaring both sides,
$\Rightarrow 243=\frac{3a^4}{16}$

$\Rightarrow a^4=81\times 16$

$\Rightarrow a=6cm$

Length of the side = 6 cm