Suppose ABC is an equilateral triangle and P is a point inside the triangle, such that PA = 3 cms., PB = 4 cms., and PC = 5 cms.
Then find the length of the side of the equilateral triangle.
The area of an equilateral triangle =.5 *a^2.9*sqrt(3).............(i)
The sum of three triangles APB, APC and BPC =.5*a*(3+4+5))...(ii)
Comparing (i) with (ii) we get a=4*sqrt(3)= 6.928