Question

A square photo of area 100 cm² is enlarged to an area of 900 cm². Find the scale factor of the side lengths of the two photos.

Answer 1

Let the side length of the original square be x cm.

Since the area of the original square is 100 cm²:
Side length of original square = x
Area of original square = x^2
100 = x^2
x = √100
x = 10 cm

Let the side length of the enlarged square be y cm.

Since the area of the enlarged square is 900 cm²:
Side length of enlarged square = y
Area of enlarged square = y^2
900 = y^2
y = √900
y = 30 cm

The scale factor of the side lengths is:
y / x = 30 cm / 10 cm = 3

Therefore, the scale factor of the side lengths of the two photos is 3.