# What is the perimeter of an equilateral triangle whose area is 25 sqrt3?

Feb 17, 2016

changed method of approach as not happy with first solution

Area is $\frac{625}{12} \sqrt{3} \cong 90.21$ to 2 decimal places

#### Explanation:

Consider the standardised equilateral triangle:

The vertical height is $\sqrt{3}$ times $\frac{1}{2}$ the base

Which is also the area. So we have for this question:

1 side =$\frac{25 \sqrt{3}}{3}$

Half of the base is $\textcolor{b r o w n}{\frac{25 \sqrt{3}}{6} \setminus}$

So the height is$\text{ } \sqrt{3} \times \frac{25 \sqrt{3}}{6} = \textcolor{b l u e}{\frac{25}{2}}$

Thus the area is $\text{ "color(blue)(25/2)color(brown)(xx(25sqrt(3))/6)" "=" } \textcolor{g r e e n}{\frac{625}{12} \sqrt{3}}$