In an equilateral triangle ABC, AE is an altitude on side BC. Show that three times square of one side of this triangle is equal to four times the square of its altitude AE.

Asked by Topperlearning User | 4th Jun, 2014, 01:23: PM

Expert Answer:

Let side of equilateral triangle be a. And AE be the altitude of ABC

So, BE = EC = =

By applying Pythagoras theorem in ABE, we have:

AB2 = AE2 + BE2

4AE2 = 3a2.

Or, 4AE2 = 3 x (square of one side)2

Hence, proved.

Answered by  | 4th Jun, 2014, 03:23: PM