Question : The area of an equilateral triangle is $4 \sqrt{3} \mathrm{~cm}^2$. Find the side (in cm) of the triangle.
Option 1: $2$
Option 2: $4$
Option 3: $\sqrt{3}$
Option 4: $2 \sqrt{3}$
Correct Answer: $4$
Solution :
It is known that the area of the equilateral triangle = $\frac{\sqrt{3}}{4}a^2$
Where $a$ is the side of the equilateral triangle.
It is given that the area of the equilateral triangle is $4\sqrt{3}$ cm$^2$
So, $\frac{\sqrt{3}}{4}a^2$ = $4\sqrt{3}$
⇒ $a^2 = 16$
⇒ $a = 4$ cm
Hence, the correct answer is 4.
.
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