Difference between revisions of "2021 AIME I Problems/Problem 2"
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Revision as of 15:57, 11 March 2021
Problem
In the diagram below, 
is a rectangle with side lengths 
and 
, and 
is a rectangle with side lengths 
and 
as shown. The area of the shaded region common to the interiors of both rectangles is 
, where 
and 
are relatively prime positive integers. Find 
.
![[asy] pair A, B, C, D, E, F; A = (0,3); B=(0,0); C=(11,0); D=(11,3); E=foot(C, A, (9/4,0)); F=foot(A, C, (35/4,3)); draw(A--B--C--D--cycle); draw(A--E--C--F--cycle); filldraw(A--(9/4,0)--C--(35/4,3)--cycle,gray*0.5+0.5*lightgray); dot(A^^B^^C^^D^^E^^F); label("$A$", A, W); label("$B$", B, W); label("$C$", C, (1,0)); label("$D$", D, (1,0)); label("$F$", F, N); label("$E$", E, S); [/asy]](http://latex.artofproblemsolving.com/c/e/7/ce7ef019f55e9d0cf7364f8d93782a020489c947.png)
Solution
See also
| 2021 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 1 |
Followed by Problem 3 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
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