MAH-CET 2026 — Mathematics PYQ

Let us solve this problem step-by-step using standard geometric formulas.

Step 1: Use the area formula to find the side length

Let the side length of the equilateral triangle be $a$ meters.

The standard formula for the area of an equilateral triangle is:

$$\text{Area}=\frac{\sqrt{3}}{4}{a}^2$$

According to the question, the given area is $400\sqrt{3}{\text{ m}}^2$. Equating the two expressions:

$$\frac{\sqrt{3}}{4}{a}^2=400\sqrt{3}$$

We can divide both sides by $\sqrt{3}$ to simplify:

$$\frac{1}{4}{a}^2=400$$

Now, multiply both sides by $4$:

$$a^2=400\times 4$$

$$a^2=1600$$

Taking the square root of both sides:

$$a=\sqrt{1600}$$

$$a=40\text{ m}$$

So, each side of the equilateral triangle measures $40\text{ meters}$.

Step 2: Calculate the perimeter of the triangle

An equilateral triangle has three equal sides. Therefore, its perimeter is the sum of all three sides:

$$\text{Perimeter}=3\times a$$

$$\text{Perimeter}=3\times 40$$

$$\text{Perimeter}=120\text{ m}$$

Conclusion

The perimeter of the equilateral triangle is $120\text{ meters}$.

Hence, the correct option is (b) 120.