Question

The volume of a prism is 100 $m^3$ and its height is $\frac{4}{\sqrt{3}}m$. The base of the prism is an equilateral triangle. What is the length of each side of the triangle forming the base of the prism ?

Answer 1

Volume of the prism = base area $\times$ height .

Since the base of the prism is an equilateral triangle, area of the base = $\frac{\sqrt{3}}{4}{s}^2$ where s is the side of the equilateral triangle.

So, $100=\frac{\sqrt{\text{/}3}}{\text{/}4}{s}^2\times \frac{\text{/}4}{\sqrt{\text{/}3}}$

$100=s^2$

s= $\sqrt{100}$

s= 10 m