# Geometric Mean Illustration

- Author:
- Tim Brzezinski

- Topic:
- Geometric Mean

**Definition:**The

**GEOMETRIC MEAN**of two numbers

*and*

**a***is defined to be the square root of their product. That is, the*

**b****GEOMETRIC MEAN**of

*and*

**a***= . In the applet below, the*

**b****purple segment that will soon appear**is the

**GEOMETRIC MEAN**of

*and*

**a**

**b****.**

**Interact with the applet for a few minutes.**Be sure to change the lengths of

*and*

**a***b*as you do. Then, answer the questions that follow.

## 1.

What is the **geometric mean** of 5 and 20?

## 2.

What is the **geometric mean** of 4 and 5?

## 3.

12 is the **geometric mean** of 36 and what other number?

## 4.

Prove that the purple segment drawn in the semicircle above has a length equal to the geometric mean of * a *and

*b*.