2009 AMC 10A Problems/Problem 17
Problem
Rectangle has and . Segment is constructed through so that is perpendicular to , and and lie on and , respectively. What is ?
Solution
The situation is shown in the picture below.
Obviously, from the Pythagorean theorem we have .
Triangle is similar to , as they have the same angles. Hence , and therefore .
Also triangle is similar to . Hence , and therefore .
We then have .
See Also
2009 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 16 |
Followed by Problem 18 | |
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 10 Problems and Solutions |