In the diagram, a smaller square lies inside a larger square. The perimeter of the smaller square is $72 \mathrm{~cm}$. The shaded area is $160 \mathrm{~cm}^{2}$. The perimeter of the larger square, in $\mathrm{cm}$, is
(A) 58
(B) 88
(C) 116
(D) 121
(E) 112

![](https://cdn.mathpix.com/cropped/2024_04_20_e85ef69091c57cb633f3g-117.jpg?height=329&width=334&top_left_y=2106&top_left_x=1468)
Since the perimeter of the smaller square is $72 \mathrm{~cm}$, its side length is $\frac{1}{4}(72)=18 \mathrm{~cm}$. Therefore, the area of the smaller square is $(18 \mathrm{~cm})^{2}=324 \mathrm{~cm}^{2}$.

Since the area inside the larger square is the combined area of the smaller square and the shaded region, then the area of the larger square is $160 \mathrm{~cm}^{2}+324 \mathrm{~cm}^{2}=484 \mathrm{~cm}^{2}$. Thus, the side length of the larger square is $\sqrt{484}=22 \mathrm{~cm}$, and so the perimeter of the larger square is $4(22 \mathrm{~cm})=88 \mathrm{~cm}$.