Purchase Solution

# Inradius of Heron triangles

Not what you're looking for?

Find all Heron triangles with inradius 1, then all heron triangles with inradius 3/2.

##### Solution Summary

This solution explains how to answer a question regarding Heron triangle.

##### Solution Preview

There are infinitely many Heronion triangles, and any one of them can be scaled by an appropriate factor to produce a new Heronian triangle with inradius 1 or 3/2, as desired.

Suppose (a, b, c) is a Heronion triangle with area A and semiperimeter s.
Then A, a, b, c, and s are rational with A^2 = s(s-a)(s-b)(s-c).

Claim: Scaling all side lengths by f = s/A results in a Heronion triangle with inradius 1.

Proof: Clearly all side lengths, and the semiperimeter, are rational after being scaled by the rational number f. The area of the scaled triangle is also rational, since ...

##### Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

##### Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

##### Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

##### Probability Quiz

Some questions on probability