A rectangle with sides 3 cm and 5 cm was enlarged in the ratio 1:3

How did the area of the rectangle change?

The ratio 1:3 means that each 1 cm is now multiplied by a factor of 3, so 3x3 = 9 and 5x3=15. Your new area is 135squarecm, and the original area was 15 square cm. You divide, so 135/15, which is 9. The area of the rectangle was increased by a factor of 9.

The area was originally 3*5, or 15 cm^2.

When the sides were enlarged, they were all multiplied by 3. The new sides are 3*3, or 9, and 5*3, or 15.

The new area is 9*15, or 135 cm^2.

If you divide 135, the new area, by 15, the original area, you get 9. So, the area increased by a factor of 9.