Question

Each side of an equilateral triangle is `6sqrt(3)` cm. The altitude of the triangle is ______.

Options

• 8 cm

• 9 cm

• `3sqrt(3)` cm

• 6 cm

Answer 1

Each side of an equilateral triangle is `6sqrt(3)` cm. The altitude of the triangle is 9 cm.

Explanation:

Area of the triangle = `(sqrt(3)/4 xx a^2)`

= `(sqrt(3)/4 xx (6sqrt(3))^2) cm^2`

= `(sqrt(3)/4 xx 108) cm^2`

= `(27sqrt(3)) cm^2`

`1/2 xx 6sqrt(3)  cm xx h = 27sqrt(3)  cm^2`

⇒ `h = (27sqrt(3))/(3sqrt(3)) cm`

⇒ h = 9 cm