2010 AMC 12B Problems/Problem 13
Problem
In ,
and
. What is
?
Solution
We note that
and
.
Therefore, there is no other way to satisfy this equation other than making both
and
, since any other way would cause one of these values to become greater than 1, which contradicts our previous statement.
From this we can easily conclude that
and
and solving this system gives us
and
. It is clear that
is a
triangle with
.
See also
2010 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 12 |
Followed by Problem 14 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |