Question

The perimeter of an equilateral triangle is $60\mathrm{m}$. 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

The correct option is D

$100\sqrt{3}{\mathrm{m}}^2$

Step 1 Given data:
Perimeter of an equilateral triangle is $60\mathrm{m}$

Step 2 Determining the sides of triangle:
Let side of equilateral triangle be $a$
So, Perimeter of the triangle$=a+a+a$
Substitute the value in above equation we get,
$$\begin{gathered} 60=3a \\ a=\frac{60}{3} \\ a=20m \end{gathered}$$

Step 3 Find the area of a triangle:
As we know,
The area of equilateral triangle can be determined by using formula: $A=\frac{\sqrt{3}}{4}{\left(side\right)}^2$
Substitute the value in above equation we get,
$$\begin{gathered} A=\frac{\sqrt{3}}{4}\left(20\right)\times \left(20\right) \\ A=100\sqrt{3}{m}^2 \end{gathered}$$
Hence, the area of an equilateral triangle is $100\sqrt{3}{m}^2.$
Therefore, option $\left(d\right)$ is the correct answer.