In an equilateral triangle ABC, D is on a side BC such that Prove that 9AD2 = 7AB2.

Question

In an equilateral triangle ABC, D is on a side BC such that  Prove that 9AD2 = 7AB2.

Philoid · Accepted Answer

Given, ABC is a equilateral triangle where AB = BC = AC and BD = BC

Draw AE perpendicular BC

⇒ Δ ABE ≅ Δ ACE

∴ BE = EC =

⇒ Now in Δ ABE, AB² = BE² + AE²

⇒ also AD² = AE² + DE²

∴ AB² –AD² = BE² – DE²

= BE² – (BE-BD)²

= ()² –

AB²-AD² = 2

Or 7 AB² = 9 AD²

Hence, proved

In an equilateral triangle ABC, D is on a side BC such that Prove that 9AD² = 7AB².