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
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
.
~MrThinker
Video Solution by OmegaLearn
https://youtu.be/jhJifWaoUI8?t=441
~ pi_is_3.14
Video Solution
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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 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
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