GeometrySection 6.1

Ratios, Proportions, and the Geometric Mean

Ratio

The ratio of a to b is Also written as a:b

Usually expressed in simplest form2 ratios that have the same simplified forms are called equivalent ratios

b

a

Examples

Simplify the ratio24 yards to 3 yards

150 cm : 6 m

The perimeter of a room is 48 feet and the ratio of its length to its width is 7 : 5. find the length and width of the room.

Using extended ratios

A triangle’s angle measures are in the extended ratio of 1 : 3 : 5. find the measures of the angles.

Proportions

An equation that states that the two ratios are equal.

Cross product property.In a proportion the product of the extremes equals the product of the means.

Examples

Solve the Proportion

8

52x

xx 3

4

3

1

147

3 yy

Example

As part of a science project, you need to estimate the number of blue spruce trees in a 50 acre forest. You count 36 trees in 3 acres and notice that the trees seem to be evenly distributed. Estimate the total number of blue spruce trees in the forest.

Geometric MeanThe geometric mean of two positive numbers a and b is the positive number x that satisfies so and b

x

x

a

abx 2 abx

Examples

Find the geometric mean of the two numbers12 and 27

18 and 54

16 and 18

Assignment

Section 6.1Page 360Problems #4 – 44 even, 50