Difference between revisions of "2020 AMC 8 Problems/Problem 25"
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==Video Solutions== | ==Video Solutions== | ||
− | https://youtu.be/KN441ecLfKM | + | https://youtu.be/KN441ecLfKM and https://youtu.be/LebVAuPkpcg |
− | https://youtu.be/LebVAuPkpcg | ||
==See also== | ==See also== |
Revision as of 14:57, 24 November 2020
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 rectangle be . We then have the system which we solve to determine .
Solution 3 (fast)
Since, for each pair of rectangles, the side lengths have a sum of or and a difference of , the answer must be .
Video Solutions
https://youtu.be/KN441ecLfKM and https://youtu.be/LebVAuPkpcg
See also
2020 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 24 |
Followed by Last Problem | |
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All AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.