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 \( s \) represent the side length of the equilateral triangle. The area is calculated using: \[\n\text{Area} = \frac{s^2 \sqrt{3}}{4}\n\] With an area of \( 4 \sqrt{3} \, \text{cm}^2 \), the equation becomes: \[\n\frac{s^2 \sqrt{3}}{4} = 4 \sqrt{3}\n\] Solving for \( s^2 \): \[\ns^2 = 16 \quad \Rightarrow \quad s = 4\n\] The perimeter is \( 3s \), hence: \[\n3 \times 4 = 12 \, \text{cm}\n\] The answer is 12 cm.