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

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

Area of an equilateral triangle.

Explanation for correct option:

The perimeter of a triangle is the sum of all the three sides of the triangle.

Since all the three sides of an equilateral triangle are equal in length.

Let us consider the side of an equilateral triangle is $x\mathrm{meters}.$

$$\begin{gathered} \therefore x+x+x=60 \\ \Rightarrow 3x=60 \\ \Rightarrow x=\frac{60}{3} \\ \Rightarrow x=20\mathrm{m} \end{gathered}$$

The area of an equilateral triangle is computed as:

$$\begin{gathered} A=\frac{\sqrt{3}}{4}\times {\left(\mathrm{side}\right)}^2 \\ =\frac{\sqrt{3}}{4}\times {\left(20\right)}^2 \\ =\frac{\sqrt{3}}{4}\times 400 \\ =100\sqrt{3}{\mathrm{m}}^2 \end{gathered}$$

Hence, Option (D) is correct.

Explanation for Incorrect option:

Since, Area of the equilateral triangle $100\sqrt{3}{\mathrm{m}}^2$ as determined above is not equal or equivalent to other Option A, Option B, or Option C.

Hence, Option A, Option B and Option C are incorrect options.

Hence, Option $\left(\mathrm{D}\right)$ is the correct option.