Activity Overview
A triangle circumscribes a rectangle. The triangle is not unique, so what is the minimum area of the triangle that circumscribes the triangle? Students use the dynamic representation on TI-Nspire, data capture and more to explore this problem with some elegant solutions.
Objectives
The purpose of this activity is for students to combine some straight forward geometry (similar triangles) to establish a formula for the area of a special triangle so they can use calculus to determine the minimum area.
Vocabulary
- Similar triangles
- Derivative (rational function)
- Minimum
About the Lesson
Students use a dynamic representation of a geometry problem, collect (generate) data and then use their equation to model the data. Once the equation is confirmed, students use differential calculus to determine the minimum area.