CEMC Gauss (Grade 7), 2006

Bogdan needs to measure the area of a rectangular carpet. However, he does not have a ruler, so he uses a shoe instead. He finds that the shoe fits exactly 15 times along one edge of the carpet and 10 times along another. He later measures the shoe and finds that it is 28 cm long. What is the area of the carpet?

(A) $150 \text{ cm}^2$ (B) $4200 \text{ cm}^2$ (C) $22\,500 \text{ cm}^2$ (D) $630\,000 \text{ cm}^2$ (E) $117\,600 \text{ cm}^2$