Question

An ant stands at one vertex of rectangular sheet of paper. The ant then proceeds to walk all the way around the perimeter of the paper. The dimensions of the sheet of paper are 3 5/8 inches by 2 7/8 inches. How many inches does the ant travel? Show your work.

Answer 1

To find the perimeter of the rectangular sheet of paper, we add up all the sides. We add $2(3 \frac{5}{8})$ to account for both the length and width of the paper. The width of the paper goes around the side 3 5/8 inches two times and the same for the length. Similarly, $2(2 \frac{7}{8})$ accounts for the vertical sides.
\begin{align*}
2(3\frac{5}{8}) + 2(2\frac{7}{8}) &=2\left(3\frac{5}{8}+2\frac{7}{8}\right)\\
&=2\left(6\frac{12}{8}\right)\\
&=2\left(7\frac{4}{8}\right)\\
&=2\left(7\frac{1}{2}\right)\\
&=2\cdot7+\frac12\cdot2\\
&=14+1\\
&=\boxed{15}\text{ inches}.
\end{align*}