The ratio of the length to the width of Rectangle A is 13:7. The ratio of the perimeter of Rectangle A to the perimeter of Rectangle B is 4:7. If the length of Rectangle A is 30 cm longer than its width, what is the perimeter of Rectangle B in cm?

cm

Set the length of Rectangle A as 13 units and the width of Rectangle A as 7 units. So, the difference between the length and width of Rectangle A is (13 – 7 = 6) units, and the perimeter of Rectangle A is

(13 + 7) × 2 = 40 units. Then,

6 units = 30

1 unit = 30 ÷ 6 = 5

40 units = 40 × 5 = 200

The perimeter of Rectangle A is 200 cm.

Then, use the method of finding an equivalent ratio to find the perimeter of Rectangle B.

4:7 = 200: ___

200 ÷ 5 = 50, so each part of 4:7 is multiplied by a common term of 50. Then,

4:7 = (4 × 50) : (7 × 50) = 200:350

Thus, the perimeter of Rectangle B is 350 cm.