Question

The perimeter of an equilateral triangle is 60 m. The 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

Given: The perimeter of an equilateral triangle is 60 m.

Let the length of the side of an equilateral triangle be x m.

$$\begin{gathered} \mathrm{Perimeter}=60\mathrm{m} \\ \Rightarrow 3x=60 \\ \Rightarrow x=\frac{60}{3} \\ \Rightarrow x=20\mathrm{m} \\ \mathrm{Area}\mathrm{of}\mathrm{an}\mathrm{equilateral}\mathrm{triangl}e=\frac{\sqrt{3}}{4}\times x^2 \\ =\frac{\sqrt{3}}{4}{\left(20\right)}^2 \\ =\frac{\sqrt{3}}{4}\left(400\right) \\ =100\sqrt{3}{\mathrm{m}}^2 \end{gathered}$$

Hence, the correct option is (d).