# Difference between revisions of "2006 AIME I Problems/Problem 1"

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So the perimeter is: | So the perimeter is: | ||

<math> 18+21+14+31=84 </math> | <math> 18+21+14+31=84 </math> | ||

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+ | The answer is 084. | ||

== See also == | == See also == |

## Revision as of 19:58, 8 March 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:

The answer is 084.