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 $28 \mathrm{~cm}$ long. What is the area of the carpet?
(A) $150 \mathrm{~cm}^{2}$
(D) $630000 \mathrm{~cm}^{2}$
(B) $4200 \mathrm{~cm}^{2}$
(E) $117600 \mathrm{~cm}^{2}$
(C) $22500 \mathrm{~cm}^{2}$
Solution 1

Since the shoe is $28 \mathrm{~cm}$ long and fits 15 times along one edge of the carpet, then one dimension of the carpet is $15 \times 28=420 \mathrm{~cm}$.

Since the shoe fits 10 times along another edge of the carpet, then one dimension of the carpet is $10 \times 28=280 \mathrm{~cm}$.

Therefore, then area of the carpet is $420 \times 280=117600 \mathrm{~cm}^{2}$.

## Solution 2

Since the shoe fits along one edge of the carpet 15 times and along another edge 10 times, then the area of the carpet is $15 \times 10=150$ square shoes.

Since the length of the shoe is $28 \mathrm{~cm}$, then

$$
1 \text { square shoe }=1 \text { shoe } \times 1 \text { shoe }=28 \mathrm{~cm} \times 28 \mathrm{~cm}=784 \mathrm{~cm}^{2}
$$

Therefore, the area of the carpet in $\mathrm{cm}^{2}$ is $150 \times 784=117600 \mathrm{~cm}^{2}$.

ANSWER: (E)