# Prove that three times the square of any side of an equilateral triangle is equal to four times the square of the altitude.

Given: In ΔABC,

AB = AC = BC

To prove: 3 AB2 = 4 AD2

Theorem Used:

1) If corresponding side and two angles of two triangles are equal the triangles are said to have SAS congruency.

2) Pythagoras theorem:

In a right-angled triangle, the squares of the hypotenuse is equal to the sum of the squares of the other two sides.

Proof:

AB = AC (given)

B = C (each 60°)

BD = DC

As ΔADB is a right triangle right angled at D.

By Pythagoras theorem,

AB2 = AD2 + (1/2 BC)2

AB2 = AD2 + (1/4 BC2)

As BC = AB

AB2 = AD2 + (1/4 AB2)

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 Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses