Difference between revisions of "2006 AIME I Problems/Problem 1"
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== Problem == | == Problem == | ||
− | In [[quadrilateral]] <math> ABCD , \angle B </math> is a right angle, diagonal <math> \overline{AC} </math> is [[perpendicular]] to <math> \overline{CD}, | + | In [[quadrilateral]] <math> ABCD</math>, <math>\angle B </math> is a [[right angle]], [[diagonal]] <math>\overline{AC}</math> is [[perpendicular]] to <math>\overline{CD}</math>, <math>AB=18</math>, <math>BC=21</math>, and <math>CD=14</math>. Find the [[perimeter]] of <math>ABCD</math>. |
== Solution == | == Solution == | ||
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[[Category:Intermediate Geometry Problems]] | [[Category:Intermediate Geometry Problems]] | ||
+ | {{MAA Notice}} |
Latest revision as of 21:43, 2 February 2014
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 I (Problems • Answer Key • Resources) | ||
Preceded by First Question |
Followed by Problem 2 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.