Question

The perimeter of an equilateral triangle whose area is \( 4\sqrt{3} \, \text{cm}^2 \) is equal to:

• A. 20 cm
• B. 10 cm
• C. 15 cm
• D. 12 cm

Hint:

Remember that for an equilateral triangle, the perimeter is simply three times the side length, and the area is related to the side by the formula \( \frac{s^2 \sqrt{3}}{4} \).

Answer 1

The Correct Option is D

Let the side of the equilateral triangle be \( s \). The area of an equilateral triangle is given by the formula: \[ \text{Area} = \frac{s^2 \sqrt{3}}{4} \] Given the area is \( 4 \sqrt{3} \, \text{cm}^2 \), we can set up the equation: \[ \frac{s^2 \sqrt{3}}{4} = 4 \sqrt{3} \] Solving for \( s^2 \): \[ s^2 = 16 \quad \Rightarrow \quad s = 4 \] The perimeter of an equilateral triangle is \( 3s \), so the perimeter is: \[ 3 \times 4 = 12 \, \text{cm} \] Therefore, the correct answer is 12 cm.