Math Example--Area and Perimeter--Triangles: Example 36

Topic

Geometry

Description

This example combines the concept of 30-60-90 right triangles with algebraic expressions. The triangle has sides labeled as x - 10 and 2(x - 10), with angles of 30 and 60 degrees. Students are challenged to use the Pythagorean Theorem to find the third side and then express the perimeter using algebraic terms.

Integrating algebra into geometric problems involving special right triangles is a key skill in advanced mathematics. This collection of examples helps teach this topic by demonstrating how algebraic expressions can represent dimensions in 30-60-90 triangles. Students learn to manipulate these expressions within the Pythagorean Theorem and perimeter formula, deepening their understanding of both algebra and geometry.

Exposure to multiple worked-out examples is vital for students to fully grasp the interplay between algebraic expressions and geometric concepts in special right triangles. Each example builds on previous knowledge, gradually increasing in complexity. This approach helps students develop problem-solving skills and recognize patterns in mathematical relationships involving variables, square roots, and ratios specific to 30-60-90 triangles.

Teacher Script: "Now we're looking at a 30-60-90 right triangle where the sides are represented by algebraic expressions. How does this change our approach to finding the third side and perimeter? Remember, we're still using the Pythagorean Theorem and the properties of 30-60-90 triangles, but now we're working with expressions instead of specific numbers. Can someone suggest how we might start this process and express the perimeter in terms of x?"

For a complete collection of math examples related to Area and Perimeter click on this link: Math Examples: Triangular Area and Perimeter Collection.