we have that Area of the enlarged square=25*a² Area of the smaller square=a²
we know that Area of the enlarged square=[scale factor]²*Area of the smaller square
solve for scale factor scale factor²=Area of the enlarged square/Area of the smaller square substitute scale factor²=(25*a²)/(a²) scale factor²=(25) scale factor=√(25) scale factor=5
therefore
the side of the enlarged square is 5 times larger than the side of the smaller square
Alternative Method
we know that Area of a square=b²------> b=√A where b is the side length of the square
for the smaller square A=a² so b=√(a²)------> b=a
for the enlarged square A=25*a² so b=√(25*a²)------> b=5a
therefore the enlarged side of the square is 5 times larger than the side of the smaller square
