Rectangle $P Q R S$ is divided into eight squares, as shown. The side length of each shaded square is 10 . What is the length of the side of the largest square?
(A) 18
(B) 24
(C) 16
(D) 23
(E) 25

![](https://cdn.mathpix.com/cropped/2024_04_20_e85ef69091c57cb633f3g-088.jpg?height=303&width=352&top_left_y=217&top_left_x=1296)
Suppose that the side length of each of the small squares is $x$. (Since the 4 small squares have the same height, they must have the same side length.)

Then the side length of the largest square is $4 x$.

Since the side length of each of the shaded squares is 10 , then $Q R=3(10)=30=P S$.

Thus, $P S=30=4 x+x$ or $5 x=30$ or $x=6$.

Therefore, the side length of the largest square is $4 x=24$.

ANSWER: (B)