Question

The perimeter of an equilateral triangle is $60m$. The area is:

• A. $10\sqrt{3}{m}^2$
• B. $15\sqrt{3}{m}^2$
• C. $20\sqrt{3}{m}^2$
• D. $100\sqrt{3}{m}^2$

Answer 1

The correct option is D

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

Explanation for the correct option:

Find the side of the equilateral triangle

We known that all three sides of the equilateral triangle are equal.

So, let the side of the equilateral triangle be $a$.

Now, perimeter of the triangle can be calculated by adding all three sides.

the perimeter of the equilateral triangle is $60m$.

So,

$$\begin{gathered} a+a+a=60 \\ \Rightarrow 3a=60 \\ \Rightarrow a=20m \end{gathered}$$

Find the area of the equilateral triangle

We known that the area of the equilateral triangle can be given as: $\frac{\sqrt{3}}{4}{a}^2$

Where $a$ is the side of the equilateral triangle.

Now, the area will be,

$$\begin{gathered} A=\frac{\sqrt{3}}{4}{\left(20\right)}^2(\because a=20m) \\ \Rightarrow A=\frac{\sqrt{3}}{4}\left(400\right) \\ \Rightarrow A=100\sqrt{3}{m}^2 \end{gathered}$$

Hence, the correct option is (d) $100\sqrt{3}{m}^2$.