Perimeter and Area of an Equilateral Triangle

Let $s$ be the side of the equilateral triangle, then:

$\begin{aligned} \dfrac{\sqrt{3}}{4}s^2 &= 25\sqrt{3} \\ \cancel{\sqrt{3}}s^2 &= 25\cancel{\sqrt{3}} \cdot 4 \\ s^2 &= 100 \\ \implies s &= 10 \end{aligned}$

Perimeter of an equilateral triangle is $3s = 3(10) = \boxed{30}$

The formula for the area of an equilateral triangle is $A=\dfrac{\sqrt{3}}{4}x^2$ where $x$ is the side length. We have

$25\sqrt{3}=\dfrac{\sqrt{3}}{4}x^2$

$100=x^2$

$10=x$

So the desired perimeter is

$P=3x=3(10)=\color{#69047E}\boxed{30~rods}$