Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 14

Topic

Ratios, Proportions, and Percents

Description

This example illustrates solving a proportion problem using similar right triangles with special angles (30°-60°-90°) and algebraic expressions. Two triangles are shown, with the smaller one having sides of 16 and 8, and the larger one having sides of (3x + 4) and 2x. The problem requires setting up a proportion: 16 / 8 = (3x + 4) / 2x. Solving this equation leads to x = 4, which then allows us to find the side lengths of 8 and 16.

Understanding proportions in geometric contexts, especially with special right triangles and 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 geometry, algebra, and trigonometry in advanced mathematical concepts.

Providing multiple worked-out examples is essential for students to fully grasp proportions and their applications in sophisticated 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, special triangles, and geometric figures.

Teacher's Script: "Let's tackle this complex proportion problem involving similar 30°-60°-90° triangles and algebraic expressions. We'll set up the proportion 16 / 8 = (3x + 4) / 2x and solve for x. Notice how we handle the algebraic terms in the context of special right triangles. This method will be useful in many advanced geometry, trigonometry, and calculus problems you'll encounter in the future, especially in fields like physics and engineering."

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