Fewpal
+2 votes
1.3k views
in Mathematics by (127k points)
edited by

In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes.

2 Answers

+2 votes
by (9.9k points)
selected by
 
Best answer

 

Let the side of the equilateral triangle be a, and AE be the altitude of ΔABC.
∴ BE = EC = BC/2 = a/2
Applying Pythagoras theorem in ΔABE, we get
AB2 = AE2 + BE2 

 

⇒ 4 × (Square of altitude) = 3 × (Square of one side)

+1 vote
by (9.9k points)

Solution: Let us assume that each side of the triangle is ‘a’, then its altitude AM is as follows:

similar triangles exercise solution

Four times of square of altitude can be calculates as follows:

similar triangles exercise solution

Hence; three times of square of a side = four times of square of altitude proved

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...