2004 AMC 12A Problems/Problem 8
Problem
In the overlapping triangles and sharing common side , and are right angles, , , , and and intersect at . What is the difference between the areas of and ?
Contents
[hide]Solution
Solution 1
If we let denote area, . Using the given, and , and their difference is .
Solution 2
Since and , . By alternate interior angles and AA~, we find that , with side length ratio . Their heights also have the same ratio, and since the two heights add up to , we have that and . Subtracting the areas, .
See also
2004 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 7 |
Followed by Problem 9 |
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All AMC 12 Problems and Solutions |