Problem 2 Finding the Geometric Mean

Multiple Choice What is the geometric mean of 6 and 15?

1. 90
2. 3 10 3 square root of 10
3. 9 10 9 square root of 10
4. 30

6 x = x 15 Definition of geometric mean x 2 = 90 Cross Products Property x = 90 Take the positive square root of each side . x = 3 10 Write in simplest radical form . table with 4 rows and 3 columns , row1 column 1 , 6 over x , column 2 equals , x over 15 , column 3 cap definitionofgeometricmean , row2 column 1 , x squared , column 2 equals 90 , column 3 cap crosscap productscap property , row3 column 1 , x , column 2 equals square root of 90 , column 3 cap takethepositivesquarerootofeachside . . , row4 column 1 , x , column 2 equals 3 square root of 10 , column 3 cap writeinsimplestradicalform . . , end table

The geometric mean of 6 and 15 is 3 10 . 3 square root of 10 .  The correct answer is B.

✓ Got It?

2. What is the geometric mean of 4 and 18?

Take note Corollary 1 to Theorem 7-3

Corollary

The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the segments of the hypotenuse.

If …

Then …

A D C D = C D D B fraction eh d , over c d end fraction . equals . fraction c d , over d b end fraction

Example

You will prove Corollary 1 in Exercise 42.