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)