Five identical rectangles are arranged to form a larger rectangle $P Q R S$, as shown. The area of $P Q R S$ is 4000 . The length, $x$, of each of the identical rectangles is closest to
(A) 35
(B) 39
(C) 41
(D) 37
(E) 33

![](https://cdn.mathpix.com/cropped/2024_04_20_6ed09463f225f8ba1f07g-106.jpg?height=304&width=347&top_left_y=412&top_left_x=1366)

## Part C: Each correct answer is worth 8.
Let $w$ be the width of each of the identical rectangles.

Since $P Q=3 w, R S=2 x$ and $P Q=R S$ (because $P Q R S$ is a rectangle), then $2 x=3 w$, or $w=\frac{2}{3} x$.

Therefore, the area of each of the five identical rectangles is $x\left(\frac{2}{3} x\right)=\frac{2}{3} x^{2}$.

Since the area of $P Q R S$ is 4000 and it is made up of five of these identical smaller rectangles, then $5\left(\frac{2}{3} x^{2}\right)=4000$ or $\frac{10}{3} x^{2}=4000$ or $x^{2}=1200$ or $x \approx 34.6$, which, of the possible answers, is closest to 35 .

ANSWER: (A)

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