Question

A square with an area of a^2 is enlarged to a square with an area of 25 a^2. How was the side of the smaller square changed?

Answer 1

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