In an equilateral triangle, prove that three times the square of one side is equal to four times the square - Maths - Triangles

Question

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

Gopal Mohanty · Accepted Answer

Let the side of the equilateral triangle be a, and AE be the altitude of ΔABC ∴ BE = EC =

=

Applying Pythagoras theorem in ΔABE, we obtain AB2 = AE2 + BE2

4AE2 = 3a2 ⇒ 4 × (Square of altitude) = 3 × (Square of one side)

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.