1998 AIME Problems/Problem 3
Contents
Problem
The graph of partitions the plane into several regions. What is the area of the bounded region?
Solution
The equation given can be rewritten as:
We can split the equation into a piecewise equation by breaking up the absolute value:
Factoring the first one: (alternatively, it is also possible to complete the square)
Hence, either , or .
Similarily, for the second one, we get or . If we graph these four equations, we see that we get a parallelogram with base 20 and height 40. Hence the answer is .
Solution 2
The equation can be rewritten as: . Do casework as above.
See also
1998 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
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