Q. 274.3( 20 Votes )

# In an equilateral

Answer :

Let the side of the equilateral triangle be a, and AE be the altitude of ΔABC To Prove : 4 × (Square of altitude) = 3 × (Square of one side)

Proof:

Altitude of equilateral triangle divides the side in two equal parts. Therefore, Pythagoras Theorem :  It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Applying Pythagoras theorem in ΔABE, we obtain

AB2 = AE2 + BE2  4 × (Square of altitude) = 3 × (Square of one side)

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Quiz- Test what you Know45 mins  Quiz- Test what you Know Part 245 mins  BPT ke Master Kaise Bane?46 mins  Pythagoras Theorem ki Application46 mins  Similarity - Apply it like a Champ45 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 RELATED QUESTIONS :

In Fig. 3,<Mathematics - Board Papers

In an equilateralRD Sharma - Mathematics