A right prism has a base that is an equilateral triangle. The height of the prism is equal to the height of the base. If the volume of the prism is 81, what are the lengths of the sides of the base?

Length of side of base is 5.45

Step-by-step explanation:

Step 1: Volume of a right prism = Area of the base * Height = 1/2 * base * height of base * height of prism

Here, since the base is an equilateral triangle and it is given that height of the prism is equal to that of the base, measures of base and height are equal.

⇒ Volume = 1/2 * b * h * h (b and h are equal)

⇒ 81 = 1/2 * b³

⇒ b³ = 162

⇒ b = ∛162 = 5.45