# Geometric Mean Exercises

### Example 1

What is the geometric mean of 1 and 4?

### Example 2

What is the geometric mean of 15 and 3?

### Example 3

What is the length of the altitude of this triangle?

### Example 4

You just bought a 20-foot tall monster TV screen that'll probably burn your retinas before you can finish an episode of Adventure Time. In fact, you have to put it on the floor because otherwise it won't fit in your room. If your eyes are at 5.5 feet and your TV is on the floor, how far away should you stand from the TV so that you can see the whole screen at once?

### Example 5

Find the length of x.

### Example 6

An animatronic bat is being built—because let's face it, who doesn't want an animatronic bat?—with wings in the shape of right triangles. The dimensions are 18 inches for the underside and 15 inches on top. To support its lifelike flight, a beam must be inserted into each wing at the altitude. How long must this beam be, to the nearest tenth of an inch?