Question

Prove that in an equilateral triangle, three time the square of a side is equal to four time the square of its altitude.

Answer 1

Let side of an equilateral triangle = a,

We kno that,

In equilateral triangle of side $a$, the altitude of triangle $=\frac{\sqrt{3}a}{2}$

$\therefore$ 4 x The square of altitude $=4\times {\left(\frac{\sqrt{3}a}{2}\right)}^2=3a^2=$ three times square of a side.

Hence proved.