Question

In an equilateral triangles ABC, AD is an altitude than 4AD² is equal to?​

Answer 1

Answer :

3AC²

Step-by-step explanation :

Let the side of the triangle be a units

Given that ∆ABC is equilateral.

So AB = BC = CA = a units

AD is the Altitude say of height 'h' units

In an equilateral triangle the altitude(AD) bisects BC.

Therefore, BD =DC = a/2

By using Pythagoras theorem,

(a/2)² + h² = a²

a²/4 + h² =a²

h² = a² - a²/4

h² = (4a² -a²)/ 4

h² = 3a²/4

4h² = 3a²

4AD² = 3AC²

HOPE THIS HELPED YOU :-)