Enlarging rectangles

Here is a rectangle with side lengths that are one centimetre and three centimetres.

Its perimeter is 8 cm and its area is 3 cm².

If we double the side lengths, what do you notice about the area of the larger rectangle?

The larger rectangle has a perimeter of 16 cm and area of 12 cm².

A rectangle with sides two times that of the original rectangle has twice its perimeter, and four times its area.

If we enlarge the original rectangle above and make the sides three centimetres and nine centimetres, we get a rectangle like this. Its area is 27 cm².

The side lengths of the rectangle are 3 cm and 9 cm, so the perimeter is 24 cm and its area is 27 cm².

A rectangle with sides three times that of the original rectangle has three times the perimeter of the original rectangle and nine times its area.