Math Example--Right Triangles-- Example 17

Topic

Right Triangles

Description

This example presents a right triangle with sides labeled x, y, and b, where the ratio of x to y is 3:5. Using the Pythagorean Theorem and given that x = 3p and y = 5p, we find that b = √((5p)² - (3p)²) = √(25p² - 9p²) = √(16p²) = 4p. This demonstrates that the triangle is a special Pythagorean Triple with sides in the ratio 3:4:5.

This example generalizes the concept of the 3-4-5 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.

Providing multiple worked examples is crucial for students to fully grasp the concept of right triangles and their various applications. Each new example offers an opportunity to explore different aspects of right triangles, helping students develop problem-solving skills and a deeper understanding of geometric relationships.

Teacher's Script: Let's examine our seventeenth example. We have a right triangle where the sides are expressed as variables in a 3:5 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 3-4-5 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.