Square $M$ has an area of $100 \mathrm{~cm}^{2}$. The area of square $N$ is four times the area of square $M$. The perimeter of square $N$ is
(A) $160 \mathrm{~cm}$
(B) $400 \mathrm{~cm}$
(C) $80 \mathrm{~cm}$
(D) $40 \mathrm{~cm}$
(E) $200 \mathrm{~cm}$
The area of square $N$ is four times the area of square $M$ or $4 \times 100 \mathrm{~cm}^{2}=400 \mathrm{~cm}^{2}$.

Thus, each side of square $N$ has length $\sqrt{400}=20 \mathrm{~cm}$.

The perimeter of square $N$ is $4 \times 20 \mathrm{~cm}=80 \mathrm{~cm}$.

ANSWER: $(\mathrm{C})$