2021 CIME I Problems/Problem 1
Problem
Let be a square. Points
and
are on sides
and
respectively
such that the areas of quadrilaterals
and
are
and
respectively. Given that
then
where
and
are relatively prime positive integers. Find
.
Solution
From the problem, we know that . Thus, the side length of the square is
. Furthermore, because
,
. Because
,
is a trapezoid. Thus, if we let
, the area of
is
. Equating this to the given area of
, we can now solve for
:
, we can now find a value for
:
Thus, our answer is .
See also
2021 CIME I (Problems • Answer Key • Resources) | ||
Preceded by First Problem |
Followed by Problem 2 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All CIME Problems and Solutions |