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 :
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 |