If the area of an equilateral triangle is $36\sqrt{3}\, cm^2$, then the length of the side is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 12 cm
Step 1: Formula for area of an equilateral triangle
$\text{Area} = \frac{\sqrt{3}}{4} a^2$
Where a = side of the triangle.
Given:
$\frac{\sqrt{3}}{4} a^2 = 36\sqrt{3}$
Step 2: Solve for $a^2$
$a^2 = \frac{36\sqrt{3} \cdot 4}{\sqrt{3}} = 36 \cdot 4 = 144$
$a = \sqrt{144} = 12 \, \text{cm}$