With six identical rectangles, we form a larger rectangle, with one of the sides measuring $21 \mathrm{~cm}$, as shown in the figure. What is the area of the larger rectangle, in $\mathrm{cm}^{2}$?
(a) 210
(b) 280
(c) 430
(d) 504
(e) 588

![](https://cdn.mathpix.com/cropped/2024_05_01_666a1aec7e447b0a6cbeg-008.jpg?height=285&width=465&top_left_y=874&top_left_x=1341)
The correct option is (e).

From the figure, we see that the length $a$ of the smaller rectangles is twice their width $b$, that is, $a=2 b$. Therefore,

$$
a+b=2 b+b=3 b=21
$$

that is, $b=7 \text{ cm}$ and $a=14 \text{ cm}$. Therefore, the length of the larger rectangle is $4 b=28$ and its area is $21 \times 28=588 \text{ cm}^{2}$.

![](https://cdn.mathpix.com/cropped/2024_05_01_666a1aec7e447b0a6cbeg-046.jpg?height=440&width=491&top_left_y=257&top_left_x=1382)