Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 18

Topic

Ratios, Proportions, and Percents

Description

This example illustrates solving a proportion problem using similar right triangles with algebraic expressions. Two right triangles are shown, with the left one having sides of 12 and 5, and the right one having sides of 10x + 8 and 5x. The problem requires setting up a proportion: 12 / 5 = (10x + 8) / 5x. Solving this equation leads to x = 4, which then allows us to find the side lengths of 20 and 48.

Understanding proportions in geometric contexts, especially with algebraic expressions, is a crucial skill in mathematics. This collection of examples helps teach the topic by presenting various scenarios where proportions are applied to solve complex problems, allowing students to see the interplay between algebra and geometry in real-world applications.

Providing multiple worked-out examples is essential for students to fully grasp proportions and their applications in advanced scenarios. Each example builds on previous concepts while introducing new elements, helping students develop problem-solving skills and recognize patterns across different types of proportion problems involving algebraic expressions and geometric figures.

Teacher's Script: "Let's tackle this more complex proportion problem involving similar right triangles and algebraic expressions. We'll set up the proportion 12 / 5 = (10x + 8) / 5x and solve for x. Notice how we handle the algebraic terms. This method will be useful in many advanced geometry and algebra problems you'll encounter in the future, especially in fields like engineering, physics, and computer graphics where complex geometric relationships are often modeled algebraically."

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