Question

In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes.

Answer 1

Data: ABC is an equilateral triangle. 

Here, AB = BC = CD. 

AD ⊥ BC.

To Prove: 3AC² = 4AD² 

In ⊥∆ADC, ∠ADC = 90° 

∴ AC² = AD² + DC²

∴ 3AC² = 4AD².