<meta http-equiv="refresh" content="1; url=/nojavascript/">
Dismiss
Skip Navigation
You are reading an older version of this FlexBook® textbook: CK-12 Foundation and Leadership Public Schools, College Access Reader: Geometry Go to the latest version.

3.7: Pythagorean Theorem, Part 2: Applications & Triples

Difficulty Level: At Grade Created by: CK-12

Learning Objectives

  • Identify common Pythagorean triples.

Using Pythagorean Triples

Review the example problems from the previous lesson.

This is the diagram from Example 1:

In Example 1, the sides of the triangle are 3, 4, and 5. This combination of numbers is referred to as a Pythagorean triple. A Pythagorean triple is three integers (whole numbers with no decimal or fraction part) that make the Pythagorean Theorem true.

  • A Pythagorean triple is a group of three _____________________________ that satisfy the Pythagorean Theorem.

Throughout this chapter, you will learn other Pythagorean triples as well.

This is the diagram from Example 2:

Using the Pythagorean Theorem equation a2+b2=c2, and letting a=6 and c=10, we calculated that b=8 inches.

The triangle in Example 2 is proportional to the same ratio of 3 : 4 : 5. If you divide the lengths of the triangle (6, 8, and 10) by 2, you find the same proportion — 3 : 4 : 5 (because 6÷2=3,8÷2=4, and 10÷2=5).

Whenever you find a Pythagorean triple, you can apply these ratios with greater factors as well.

Finally, look at the side lengths of the triangle in Example 3:

The two legs are 5 cm and 12 cm and the length of the missing side (the hypotenuse) is 13 cm. The side lengths make a ratio of 5 : 12 : 13. This, too, is a Pythagorean triple. You can infer that this ratio, multiplied by greater factors, will also yield numbers that satisfy the Pythagorean Theorem.

There are infinitely many Pythagorean triples, but a few of the most common ones and their multiples are in the chart below:

Pythagorean triple ×2 ×3 ×4
3 – 4 – 5 6 – 8 – 10 9 – 12 – 15 12 – 16 – 20
5 – 12 – 13 10 – 24 – 26 15 – 36 – 39 20 – 48 – 52
7 – 24 – 25 14 – 48 – 50 21 – 72 – 75 28 – 96 – 100
8 – 15 – 17 16 – 30 – 34 24 – 45 – 51 32 – 60 – 68

Reading Check:

1. What is a Pythagorean triple?

2. Which of the following is NOT a Pythagorean triple? Show your work.

a. 15 – 36 – 39

b. 15 – 20 – 25

c. 16 – 30 – 35

d. 25 – 60 – 65

3. Give 2 examples of Pythagorean triples that are NOT in the chart above.

4. Why is it helpful to know common Pythagorean triples?

Image Attributions

You can only attach files to None which belong to you
If you would like to associate files with this None, please make a copy first.

Reviews

Please wait...
Please wait...
Image Detail
Sizes: Medium | Original
 

Original text