Mock AIME 1 Pre 2005 Problems/Problem 12
Problem
is a rectangular sheet of paper. and are points on and respectively such that . If is folded over , maps to on and maps to such that . If and , then the area of can be expressed as square units, where and are integers and is not divisible by the square of any prime. Compute .
Solution
Let . By some angle chasing in , we find that . Before we apply the law of sines, we're going to want to get everything in terms of , so note that . Now, we use law of sines, which gives us the following:
, but since , we go with the positive solution. Thus, .
Denote the intersection of and with . By another application of the law of sines, and . Since , and . Note that , so .
Now we have that , and . Thus, the area of is , and our final answer is .
See also
Mock AIME 1 Pre 2005 (Problems, Source) | ||
Preceded by Problem 11 |
Followed by Problem 13 | |
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