Quadratic Equations On Triangles With The Pythagorean Theorem
Hi there. This math post focuses on quadratic equations on triangles with the Pythagorean Theorem. It is assumed that the reader is familiar with the Pythagorean Theorem, expanding binomial expressions (FOIL method), factoring quadratic equations and solving quadratic equations.
This guide will feature examples with worked through solutions. You can read along or try to solve the example questions and then see the answers.
The triangle pictures are from my phone and the screenshot image answers to the examples are rendered in RMarkdown.
Example One
There is a right angled triangle with the hypotenuse length being 2x - 1. The legs of this right triangle have lengths of x and x + 1. A picture can be seen below.
What is a possible value for x?
Answer
Example Two
Consider the right angled triangle with its side lengths below.
Compute the area of the triangle.
Answer
Great problems like the way you increased the level of difficulty from one problem to the next.
I like having the progression in difficulty in my guides.