Question

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

Answer 1

Answer:

Let the side of the equilateral triangle be a

Drop perpendicular from one vertex A to it's opposite side BC at D, then this is the height =h

Now ADB is a right angle triangle where AB=a is hypotenuse, h is one leg and a/2 is another leg

Apply now Pythagoras theorem

a square =h square+ (a/2) square

a square-(a/4) square= h square

(3/4) a square = h square