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 vol

Question

3 years ago

11

ume of the prism is 81, what are the lengths of the sides of the base?

1 answer:

Romashka [77] · Answer 1 · 2022-09-02T01:59:27+03:00

Answer:

Lengths of the sides (there are 3 sides in an equilateral triangle) of the base of prism is 5.72cm each.

Step-by-step explanation:

As the base of triangular prism is equilateral:

∴ Area of base = (√ 3 / 4)× (side)²

According to question:

height of prism = height (side) of base

Volume of prism = 81 cm³,

∴ Volume of prism = Area of base x height

⇒ 81 cm³ = (√ 3 / 4)× (side)² × height ∵ side = height

⇒ 81 cm³ = (√ 3 / 4)× (side)³

⇒ 81 × (4/√3) cm³ = side³

⇒ ∛(81 × (4/√3) cm = side

⇒ side = 5.72cm