A rectangular sheet of paper measures $25 \mathrm{~cm}$ by $9 \mathrm{~cm}$. The dimensions of a square sheet of paper with the same area are
(A) $15 \mathrm{~cm}$ by $15 \mathrm{~cm}$
(D) $17 \mathrm{~cm}$ by $17 \mathrm{~cm}$
(B) $8 \mathrm{~cm}$ by $8 \mathrm{~cm}$
(C) $34 \mathrm{~cm}$ by $34 \mathrm{~cm}$
Since the rectangular sheet of paper measures $25 \mathrm{~cm}$ by $9 \mathrm{~cm}$, its area is $25 \times 9$ or $225 \mathrm{~cm}^{2}$. A square sheet of paper has equal length and width.

If the length and width of the square is $s$, then the area of the square is $s \times s$ or $s^{2}$. Therefore $s^{2}=225$, or $s=\sqrt{225}=15$ (since $s$ is a positive length).

The dimensions of the square sheet of paper having the same area are $15 \mathrm{~cm}$ by $15 \mathrm{~cm}$.

ANSWER: (A)