Geometric Mean Illustration
Definition:
The GEOMETRIC MEAN of two numbers a and b is defined to be the square root of their product.
That is, the GEOMETRIC MEAN of a and b = .
In the applet below, the purple segment that will soon appear is the GEOMETRIC MEAN of a and b.
Interact with the applet for a few minutes. Be sure to change the lengths of a and 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.