2020 AMC 8 Problems/Problem 25
Contents
- 1 Problem
- 2 Solution 1
- 3 Solution 2
- 4 Solution 3 (faster version of Solution 1)
- 5 Solution 4
- 6 Video Solution(🚀Just 1 min🚀)
- 7 Video Solution
- 8 Video Solution by OmegaLearn
- 9 Video Solution by WhyMath
- 10 Video Solution by The Learning Royal
- 11 Video Solution by Interstigation
- 12 Video Solution by STEMbreezy
- 13 See also
Problem
Rectangles and and squares and shown below, combine to form a rectangle that is 3322 units wide and 2020 units high. What is the side length of in units?
Solution 1
Let the side length of each square be . Then, from the diagram, we can line up the top horizontal lengths of , , and to cover the top side of the large rectangle, so . Similarly, the short side of will be , and lining this up with the left side of to cover the vertical side of the large rectangle gives . We subtract the second equation from the first to obtain , and thus .
Solution 2
Assuming that the problem is well-posed, it should be true in the particular case where and . Let the sum of the side lengths of and be , and let the length of square be . We then have the system which we solve to determine .
Solution 3 (faster version of Solution 1)
Since, for each pair of rectangles, the side lengths have a sum of or and a difference of , the answer must be .
Solution 4
Let the side length of be s, and the shorter side length of and be . We have
From this diagram, it is evident that . Also, the side length of and is . Then, . Now, we have 2 systems of equations.
We can see an in the 2nd equation, so substituting that in gives us .
Video Solution(🚀Just 1 min🚀)
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Video Solution
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https://www.youtube.com/watch?v=gJXMZq2Rbwg ~David
Video Solution by OmegaLearn
https://youtu.be/jhJifWaoUI8?t=441
~ pi_is_3.14
Video Solution by WhyMath
~savannahsolver
Video Solution by The Learning Royal
Video Solution by Interstigation
https://youtu.be/YnwkBZTv5Fw?t=1639
~Interstigation
Video Solution by STEMbreezy
https://youtu.be/wq8EUCe5oQU?t=588
~STEMbreezy
See also
2020 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 24 |
Followed by Last Problem | |
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