There is a point inside an equilateral triangle which is at distance 3, 4, 5 from the three sides. The area of
the triangle is..

If a is the side, then area=(a/2)(3+4+5)=6a

Semi perimeter =(3/2)a

Area using Heron’s formula=sqrt(3/2a.1/2a.1/2a.1/2a)=root3/4.a^2

Hence root3/4.a^2=6a

a=8root3

Area=48root3

Regards

Arun (askIIITians forum expert)