2020 AMC 8 Problems/Problem 25
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 find that
.
Solution 3 (fast)
Since each pair of boxes has a sum of or
and a difference of
, we see that the answer is
.
See also
2020 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 24 |
Followed by Last Problem | |
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