Prove that, given a triangle with sides $a,b,c$, there exists a triangle with sides $a+2b,b+2c,c+2a$ that has an area three times the original

Question

Prove that, given a triangle with sides $a,b,c$, there exists a triangle with sides $a+2b,b+2c,c+2a$ that has an area three times the original

I have used Heron's formula but got lost in algebra! Any one got other approach?

Answer 1

Assume the original triangle is an equilateral triangle with side $s$, then the new triangle is also equilateral with sides $3s$.

The area of the new triangle is $9$ times the area of the original, not $3$ times.

Thus the statement is not true in general.