Question

The length of each side of an equilateral triangle having an area of 9√3 cm² is

Answer 1

6 cm

Explanation:

Let each side of the equilateral triangle be a.

Given, area of an equilateral triangle = 9√3 cm2

Area of an equilateral triangle = (√3)/4 × (Side)²

=> (√3)/4 × a² = 9√3

`{a}^(2) = (9 √(3) )/( ( √(3) )/(4) ) = (9 √(3) )/( √(3) ) * 4 = 9 * 4`

=> a² = 36

`\sqrt{ {a}^(2) } = √(36) \\ a = (+ - )6`

∴ Side = 6 cm [taking positive square root because side is always positive]