1. 6.1 – Ratios, Proportions, and the Geometric Mean
If a and b are two numbers or quantities and b does not equal zero, then the ratio of a to b is a/b. The ratio of a to b can also be written as a:b.
For example, the ratio of a side length of Triangle ABC to a side length in Triangle DEF can be written as 2/1 or 2:1.

2. 6.1 – Ratios, Proportions, and the Geometric Mean
Example 1:
Simplify the ratio.
a. 64 m: 6 m b. 5 ft / 20 in

3. 6.1 – Ratios, Proportions, and the Geometric Mean
Example 1:
Simplify the ratio.
c. 24 yds to 3 yds d cm: 6 m

4. 6.1 – Ratios, Proportions, and the Geometric Mean
Example 2:
You are planning to paint a mural on a rectangular wall. You know that the perimeter of the wall is 484 feet and that the ratio of its length to its width is 9:2. Find the area of the wall.

5. 6.1 – Ratios, Proportions, and the Geometric Mean
Example 3:
The measures of the angles in Triangle CDE are in the extended ratio of 1:2:3. Find the measures of the angles.

6. 6.1 – Ratios, Proportions, and the Geometric Mean
Example 4:
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.

7. 6.1 – Ratios, Proportions, and the Geometric Mean
Example 5:
The measures of the angles in Triangle CDE are in the extended ratio of 1:3:5. Find the measures of the angles.

8. 6.1 – Ratios, Proportions, and the Geometric Mean
An equation that states that two ratios are equal is called a proportion.
The numbers b and c are the means of the proportion. The numbers a and d are the extremes of the proportion.

9. 6.1 – Ratios, Proportions, and the Geometric Mean

10. 6.1 – Ratios, Proportions, and the Geometric Mean
Example 6: Solve the proportion.

11. 6.1 – Ratios, Proportions, and the Geometric Mean
Example 7: Solve the proportion.
As part of an environmental study, you need to estimate the number of trees in a 150 acre area. You count 270 trees in a 2 acre area and you notice that the trees seem to be evenly distributed. Estimate the total number of trees.

12. 6.1 – Ratios, Proportions, and the Geometric Mean

13. 6.1 – Ratios, Proportions, and the Geometric Mean
Example 8:
Find the geometric mean of 24 and 48.
Find the geometric mean of 12 and 27.