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Pythagorean Triples

Indirect measurement applications

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The Builder's Triangle

Credit: Giles Douglas
Source: http://www.flickr.com/photos/orangelimey/2237391242/
License: CC BY-NC 3.0

Do you remember the story of the Three Little Pigs? The Big Bad Wolf had no problem blowing down the houses of two of the pigs. One of the pigs, however, had a sturdy house. Carpenters use a unique rule to make sure that the rooms of your house are well built.

The Math Connection

In order to make sure that the corner of a room is square, builders need to create a 90-degree angle in the corner. How can they do this? They use a special calculation, called the 3-4-5 rule. This rule reminds them to measure three feet from the corner in one direction and four feet from the corner in the other direction. Next, the builder measures the distance between the two marks. The distance equals five if the corner is square. Have you guessed how it works?

Credit: Laura Guerin
Source: CK-12 Foundation
License: CC BY-NC 3.0

If you imagined the three- and four-foot measurements as legs of a triangle, you might have guessed that the builder is using the Pythagorean theorem. The third measurement should be five: \begin{align*}3^2+4^2=5^2\end{align*}. If the third measurement is greater than five feet, the angle has a measurement of more than 90 degrees. If the measurement is less than five feet, the angle measurement is less than 90 degrees. Only a 90-degree angle produces a perfect corner. Builders try to get as close to perfect as possible!

See for yourself: http://woodworking.about.com/od/gettingstarted/qt/345Rule.htm

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Watch the following video to learn more about the 3-4-5 rule.


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Image Attributions

  1. [1]^ Credit: Giles Douglas; Source: http://www.flickr.com/photos/orangelimey/2237391242/; License: CC BY-NC 3.0
  2. [2]^ Credit: Laura Guerin; Source: CK-12 Foundation; License: CC BY-NC 3.0

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