Rectangles $R_1$ and $R_2$, and squares $S_1$, $S_2$, and $S_3$, shown below, combine to form a rectangle that is $3322$ units wide and $2020$ units high. What is the side length of $S_2$ in units?

A. 651

B. 655

C. 656

D. 662

E. 666

1. 2020 AMC 8 官方解析

Let $x_1$, $x_2$, and $x_3$ represent the side lengths of squares $S_1$, $S_2$, and $S_3$, respectively. Then the width of the large rectangle equals
$x_1 + x_2 + x_3 = 3322$
and the height of the large rectangle equals
$x_1 - x_2 + x_3 = 2020.$
Subtracting the two equations yields $2x_2 = 1302$, so $x_2 = 651$. The side length of $S_2$ is therefore $651$ units.

Note: Although the size of square $S_2$ is fixed, the sizes of $S_1$ and $S_3$ can vary as long as the sum of their side lengthsis $x_1 + x_3 = 3322 - x_2 = 2671$.

令$x_1$，$x_2$和$x_3$分别代表正方形$S_1$，$S_2$和$S_3$的边长．那么大长方形的宽度等于
$x_1 + x_2 + x_3 = 3322$
大长方形的高度等于
$x_1 - x_2 + x_3 = 2020.$
将两个方程式相减得出$2x_2 = 1302$，因此$x_2 = 651$ 因此$S_2$的边长为$651$个单位．

注意：尽管正方形$S_2$的大小是固定的，但$S_1$和$S_3$的大小可以变化，只要满足
$x_1 + x_3 = 3322 - x_2 = 2671$．