Q. 164.2( 6 Votes )

Find the length of the altitude of an equilateral triangle of side 2a cm.

Answer :


Let ABC be the equilateral triangle whose side is 2a cm.


Let us draw altitude AD such that AD BC.


We know that altitude bisects the opposite side.


So, BD = DC = a cm.


In ADC, ADC = 90°.


We know that the Pythagoras Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.


So, by applying Pythagoras Theorem,


AC2 = AD2 + DC2


(2a cm)2 = AD2 + (a cm)2


4a2 cm2 = AD2 + a2 cm2


AD2 = 3a2 cm2


AD = √3 a cm


The length of altitude is √3 a cm.


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
Champ Quiz | Thales Theorem49 mins
NCERT | Strong Your Basics of Triangles39 mins
RD Sharma | Imp. Qs From Triangles41 mins
R.D Sharma | Solve Exercise -4.2 and 4.3FREE Class
Quiz | Criterion of Similarity of Triangle45 mins
How to Ace Maths in NTSE 2020?36 mins
R.D Sharma | Solve Exercise-4.545 mins
NCERT | Basic Proportionality Theorem22 mins
RD Sharma | Imp Qs Discussion- Triangles43 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