Math Example--Right Triangles-- Example 20

Topic

Right Triangles

Description

This example features a right triangle with sides labeled x, y, and b, where the ratio of x to y is 5:13. Using the Pythagorean Theorem and given that x = 5p and y = 13p, we find that b = √((13p)² - (5p)²) = √(169p² - 25p²) = √(144p²) = 12p. This demonstrates that the triangle is a special Pythagorean Triple with sides in the ratio 5:12:13.

This example generalizes the concept of the 5-12-13 Pythagorean triple, showing how it can be expressed algebraically for any scale factor p. It helps students understand the algebraic representation of geometric relationships and how variables can be used to express general rules in mathematics.

Exposing students to multiple worked examples is essential for developing a comprehensive understanding of right triangles and their properties. Each new example provides an opportunity to explore different aspects of right triangles, helping students recognize patterns and build problem-solving skills that can be applied to various geometric scenarios.

Teacher's Script: Now, let's look at our twentieth example. We have a right triangle where the sides are expressed as variables in a 5:13 ratio. How is this different from our previous examples? That's right, we're looking at a general case. Our task is to express b in terms of p. As we work through this, think about how this relates to the 5-12-13 triangles we've seen. How does using variables help us understand the general properties of this special Pythagorean triple?

For a complete collection of math examples related to Right Triangles click on this link: Math Examples: Right Triangles Collection.