Sixteen squares are arranged to form a region, as shown.

Each square has an area of $400 \mathrm{~m}^{2}$. Anna walks along the path $\_$formed by the outer edges of the region exactly once. Aaron walks along the path -..... formed by the inner edges of the region exactly once. In total, how far did Anna and Aaron walk?
(A) $160 \mathrm{~m}$
(B) $240 \mathrm{~m}$
(C) $320 \mathrm{~m}$
(D) $400 \mathrm{~m}$
(E) $640 \mathrm{~m}$

![](https://cdn.mathpix.com/cropped/2024_04_20_6ed09463f225f8ba1f07g-051.jpg?height=298&width=292&top_left_y=821&top_left_x=1342)
Each of the squares that has area $400 \mathrm{~m}^{2}$ has side length $\sqrt{400}=20 \mathrm{~m}$.

Anna's path walks along exactly 20 side lengths of squares, so has length $20 \cdot 20=400 \mathrm{~m}$. Aaron's path walks along exactly 12 side lengths of squares, so has length $12 \cdot 20=240 \mathrm{~m}$. Therefore, the total distance that they walk is $400+240=640 \mathrm{~m}$.

ANSWER: (E)