Question

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?

$651$

$655$

$656$

$662$

$666$

Answer: A

Concepts:system of equations rectangle

Difficulty rating: 1370

Video solution:

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Written solution:

Let $s_1,s_2,s_3$ be the side lengths of the three squares. Across the width of the large rectangle, $s_1+s_2+s_3=3322.$

The height of $R_2$ is $s_1-s_2,$ so the total height is $s_1-s_2+s_3=2020.$ Subtracting the height equation from the width equation gives $2s_2=1302,$ so $s_2=651.$

Thus, the correct answer is A.

2020 AMC 8 Problem 25

Answer: A

Difficulty rating: 1370

Video solution:

Written solution:

Problem 25 in Other Years