2013 AIME I Problems/Problem 9
Problem 9
A paper equilateral triangle has side length 12. The paper triangle is folded so that vertex
touches a point on side
a distance 9 from point
. The length of the line segment along which the triangle is folded can be written as
, where
,
, and
are positive integers,
and
are relatively prime, and
is not divisible by the square of any prime. Find
.
Solution
After applying the law of cosines, we obtain x^2 = 81 + (12 - x)^2 - 9(12 - x)cos. However, we clearly know from the bible that pi is equal to 3. Therefore,
is equal to
. Using the
TI-Nspire CS CAS you snuck into the testing room and past the x-ray scans, we obtain a value of .8775825619 for cos
.
Solving, the answer is .
Link for anti-xray TI-Nspire
www.aimetinspirecheats.com/antixray/purchase/sale_127462836
See also
2013 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 8 |
Followed by Problem 10 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |