2020 AMC 8 Problems/Problem 25
Contents
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 (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
Assuming that the problem is well-posed, it should be true in the case where . Let the side length of square be and the side length of square be . We then have the system and we solve it to determine that .
Video Solution
https://www.youtube.com/watch?v=a3Z7zEc7AXQ
Video Solution by WhyMath
~savannahsolver
Video Solution by The Learning Royal
Video Solution by Interstigation
https://youtu.be/YnwkBZTv5Fw?t=1639
~Interstigation
See also
2020 AMC 8 (Problems • Answer Key • Resources) | ||
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