In the diagram, rectangle $P Q R S$ is divided into three identical squares. If $P Q R S$ has perimeter $120 \mathrm{~cm}$, what is its area, in $\mathrm{cm}^{2}$ ?
(A) 225
(B) 675
(C) 360
(D) 432
(E) 144

![](https://cdn.mathpix.com/cropped/2024_04_20_6ed09463f225f8ba1f07g-111.jpg?height=200&width=390&top_left_y=2044&top_left_x=1277)
Let the side length of each of the squares be $x$.

![](https://cdn.mathpix.com/cropped/2024_04_20_faa9db06d997f2a5b9b1g-183.jpg?height=195&width=391&top_left_y=1163&top_left_x=932)

Then the perimeter of $P Q R S$ equals $8 x$, so $8 x=120 \mathrm{~cm}$ or $x=15 \mathrm{~cm}$.

Since $P Q R S$ is made up of three squares of side length $15 \mathrm{~cm}$, then its area is $3(15 \mathrm{~cm})^{2}$ or $3(225) \mathrm{cm}^{2}=675 \mathrm{~cm}^{2}$.

ANSWER: (B)