Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 23

Topic

Ratios, Proportions, and Percents

Description

This example demonstrates solving a proportion problem using similar equilateral triangles. Two equilateral triangles are shown, with the smaller one having a side length of 12, and the larger one having a side length of 6x and an additional side labeled as 12 + x. The problem requires finding the lengths of the sides of the larger triangle by setting up a proportion: 12 / 12 = (12 + x) / 6x. Solving this equation leads to x = 2.4, and the length of the larger triangle's side is found to be approximately 14.4 units.

Understanding proportions in geometric contexts, particularly with equilateral triangles, is a crucial skill in mathematics. This collection of examples helps teach the topic by presenting various scenarios where proportions are applied to solve problems involving special triangles, allowing students to see the connection between geometry, algebra, and trigonometry.

Exposure to multiple worked-out examples is essential for students to fully grasp proportions and their applications in advanced geometric scenarios. Each example reinforces the core concept while introducing different aspects of special triangles, helping students develop problem-solving skills and recognize patterns across various types of proportion problems involving equilateral triangles and their unique properties.

Teacher's Script: "In this example, we're working with equilateral triangles, which have all sides equal and all angles equal to 60°. Let's use this knowledge to set up our proportion and solve for the side lengths. This skill is particularly useful in trigonometry and calculus, as well as in fields like physics and engineering where understanding the properties of equilateral triangles is crucial for solving complex problems."

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