2020 AMC 8 Problem 25

Attempt Problem 25 of the 2020 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2020 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

25.

Rectangles R1R_1 and R2,R_2, and squares S1,S_1, S2,S_2, and S3,S_3, shown below, combine to form a rectangle that is 33223322 units wide and 20202020 units high. What is the side length of S2S_2 in units?
651651
655655
656656
662662
666666
Answer: A
Concepts:system of equationsrectangle
Small hint:
Let the square side lengths be s1,s2,s3s_1,s_2,s_3
Big hint:
Subtract the height equation from the width equation
Video solution:
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Written solution:
Let s1,s2,s3s_1,s_2,s_3 be the side lengths of the three squares. Across the width of the large rectangle, s1+s2+s3=3322. s_1+s_2+s_3=3322.
The height of R2R_2 is s1−s2,s_1-s_2, so the total height is s1−s2+s3=2020. s_1-s_2+s_3=2020. Subtracting the height equation from the width equation gives 2s2=1302,2s_2=1302, so s2=651.s_2=651.
Thus, the correct answer is A.
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