If the area of an equilateral triangle is $$\frac{\sqrt{3}}{2} \times 84.5 \ \text{cm}^2$$, then each side of the triangle is: 

Correct option is D

Given: ​

Area of equilateral triangle = $$\frac{\sqrt{3}}{2} \times 84.5 \ \text{cm}^2$$ 

Formula Used: ​

Area of equilateral triangle = $$\frac{\sqrt3}{4} \times \text{side}^2$$ 

Solution: ​

Using the formula;

​$$\frac{\sqrt{3}}{2} \times 84.5 \ \text{cm}^2 = \frac{\sqrt{3}}{4} \times \text{side}^2 \\ \ \\ \implies \text{side}^2 = 84.5 \times 2 = 169 \\ \ \\ \text{side} = \sqrt{169} = 13 cm$$​​