Difference between revisions of "2006 AIME A Problems/Problem 1"
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[[Category:Intermediate Geometry Problems]] | [[Category:Intermediate Geometry Problems]] | ||
Revision as of 14:54, 25 September 2007
Problem
In quadrilateral 
is a right angle, diagonal 
is perpendicular to 
and 
Find the perimeter of 
Solution
From the problem statement, we construct the following diagram:
Using the Pythagorean Theorem:
Substituting 
for 
:
Plugging in the given information:
So the perimeter is 
, and the answer is 
.
See also
| 2006 AIME II (Problems • Answer Key • Resources) | ||
| Preceded by First Problem |
Followed by Problem 2 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
