Question

If the perimeter of an equilateral triangle is 60 m, then its area is

(a) $10\sqrt{3}{\mathrm{m}}^2$

(b) $15\sqrt{3}{\mathrm{m}}^2$

(c) $20\sqrt{3}{\mathrm{m}}^2$

(d) $100\sqrt{3}{\mathrm{m}}^2$

Answer 1

Let a be the side of the equilateral triangle. Then
Perimeter = 60 m
$$\begin{gathered} \Rightarrow a+a+a=60 \\ \Rightarrow 3a=60\Rightarrow a=20\mathrm{m} \end{gathered}$$
Now
$\mathrm{Area}=\frac{a^2\sqrt{3}}{4}=\frac{{\left(20\right)}^2\sqrt{3}}{4}=\frac{400\sqrt{3}}{4}=100\sqrt{3}{\mathrm{m}}^2$
Hence, the correct option is (d).