what is the % increase in the area of the triangle if each side is doubled?

Let the sides of the triangle be x,y,z

Using the Heron's formula Are of that triangle

= A =S(S-x)(S-y)(S-z)     where S = (x+y+z)/2 , the semiperimeter.

The New triangle has sides 2x,2y,2z

So S' = (2x+2y+2z)/2 =x+y+z = 2S

  A' = 2S(2S-2x)(2S-2y)(2S-2z)  =4A

Incrtease in Area =  4S - S  = 3S

Percentage Increase in Area = 3S/S   *   100  =  300 percent