operationsto solvethe equation,and alwayskeepboth sidesof the equation“balanced”.
In algebrayou learnedthat because,for example,. However, in this
case(and in muchof geometry),we are only interestedin the positivesolutionto becausegeo-
metriclengthsare positive.So, in example2, we can disregardthe solution , and our final answer
is inches.
Example 3
Find the lengthof the missingside in the trianglebelow.Use the PythagoreanTheoremto set up an equationand solvefor the missingside. Let and
.
So, the lengthof the missingside is 13 centimeters.UsingPythagoreanTriples
In example1, the sidesof the trianglewere , , and. This combinationof numbersis referredto as a
Pythagoreantriple. A Pythagoreantripleis threenumbersthat makethe PythagoreanTheoremtrue and
they areintegers(wholenumberswith no decimalor fractionpart).Throughoutthis chapter, you will use
otherPythagoreantriplesas well. For instance,the trianglein example2 is proportionalto the sameratio
of. If you dividethe lengthsof the trianglein example 2 by two, you find the same
proportion—. Wheneveryou find a Pythagoreantriple,you can applythoseratioswith greater
factorsas well. Finally, take note of the side lengthsof the trianglein example3—. This,too,