Question

Each side of an equilateral triangle is 10 cm. The length of the each its altitude is ______.

विकल्प

• 5 cm

• `5sqrt(2)  cm`

• `5sqrt(3)  cm`

• `3sqrt(5)  cm`

Answer 1

Each side of an equilateral triangle is 10 cm. The length of the each its altitude is `underlinebb(5sqrt(3) cm)`.

Explanation:

Drop an altitude, it splits the equilateral triangle into two 30° – 60° – 90° right triangles with base half = 5 cm and hypotenuse 10 cm.

Using Pythagoras,

Altitude = `sqrt(10^2 - 5^2)`

= `sqrt(100 - 25)`

= `sqrt(75)`

= `5sqrt(3)  cm`

Equivalently 

`h = sqrt(3)/2 xx 10` 

= `5sqrt(3)`