video explanation

text explanation

remember that the multiply for a 50% increase, or 50% greater, is (1 + .50) = 1.5  

we are told that de = (1.5)ab, and by extension, every length in triangle def is 1.5 times the corresponding length in triangle abc.  the scale factor is this multiplier, k = 1.5.  

there is a formula for the exact area of an equilateral triangle, but you don’t need that here.  for any triangle, a = (0.5)bh—in fact, any area formula in geometry somehow involves a length times a length.  if each length is multiplied by k = 1.5, then any area would be multiplied by k² = (1.5)²; areas are always multiplied by the scale factor squared. 

to square, it’s easy to change to a fraction:

(1.5)² =  = = 2.25  

the area of triangle abc multiplied by 2.25 equals the area of triangle def.  this number, 2.25 = 1 + 1.25, is the multiplier for a 125% increase, so that the percentage increase of the area.  

answer = (c)