If the side length is increased by a factor by of 3 , how much larger is the perimeter of a face of the new cube

We are given in the problem a quadrilateral which is a square and the dimensions of the sides. A square is a quadrilateral with four equal sides and perpendicular angles on all corners. The perimeter of a polygon is equal to the sum of the sides of the polygon. hence, for a square, the formula of the perimeter is four times the length. Thus,

P1 = 4s 

when s is increased by a factor of 3, that is s*3 = 3s, then

P2 = 4*(3*s)= 12s

The ratio of the two perimeters is P2/P1 = 12s/4s = 3

The answer to this question is 3.