Q. 254.6( 12 Votes )

# In an equilateral triangle ABC, AD is the altitude drawn from A on side BC. Prove that 3AB^{2}= 4AD^{2}.

Answer :

Given: ABC is an equilateral triangle

and AD is the altitude on side BC

To Prove: 3AB^{2}= 4AD^{2}

In right triangle ∆ADB, using Pythagoras theorem

**(Perpendicular) ^{2} + (Base)^{2} = (Hypotenuse)^{2}**

⇒ AD^{2} + BD^{2} = AB^{2}

⇒ 4AD^{2} + BC^{2} = 4AB^{2}

⇒ 4AD^{2} = 4AB^{2} – BC^{2}

⇒ 4AD^{2} = 4AB^{2} – AB^{2} [∵ABC is an equilateral triangle]

⇒ 4AD^{2} = 3AB^{2}

Hence Proved

Rate this question :

How useful is this solution?

We strive to provide quality solutions. Please rate us to serve you better.

Related Videos

Basic Proportionality Theorem42 mins

A Peep into Pythagoras Theorem43 mins

R.D Sharma | Solve Exercise -4.2 and 4.3FREE Class

NCERT | Strong Your Basics of Triangles39 mins

RD Sharma | Imp. Qs From Triangles41 mins

Champ Quiz | Thales Theorem49 mins

NCERT | Concept Based Questions on Triangles31 mins

Quiz | Criterion of Similarity of Triangle45 mins

How to Ace Maths in NTSE 2020?36 mins

Know About Important Proofs in Triangles33 mins

Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Expertsview all courses

Dedicated counsellor for each student

24X7 Doubt Resolution

Daily Report Card

Detailed Performance Evaluation