Lesson: Geometry - 15

Popular Pythagorean Ratios

[Page 15 of 30]

There are two Pythagorean theorem ratios that test makers use again and again. One is the ratio you saw on the previous problem, in which the legs had lengths of 3 and 4, and the hypotenuse had length 5. These integers form the most common ratio; you'll see it all the time! Any time that you see a right triangle with two of the three components, you'll know the other one without having to calculate it.

Because this relationship is a ratio, it also works if we increase the size of each component proportionately. Be on the lookout for triangles with sides that are multiples of 3:4:5, like those with sides 6:8:10 or 9:12:15.

The other common ratio is 5:12:13, and you may see multiples of it as well.

Learn to recognize the 3:4:5 and 5:12:13 ratios in order to find lengths for these special triangles instantly, without calculations.

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