Beginning Algebra, 11th Edition

Two triangles are similarif they have the same shape (but not

necessarily the same size). Similar triangles have sides that are

proportional. The figure shows two similar triangles. Notice that

the ratios of the corresponding sides all equal :

If we know that two triangles are similar, we can set up a proportion to solve for the length of

an unknown side.

Use a proportion to find the lengths x and y in each pair of similar triangles.

66. 67. 68.

For Exercises 69 and 70, (a)draw a sketch consisting of two right triangles depicting the

situation described, and (b)solve the problem. (Source: Guinness World Records.)

69.An enlarged version of the chair used by George Washington at the Constitutional

Convention casts a shadow 18 ft long at the same time a vertical pole 12 ft high casts a

shadow 4 ft long. How tall is the chair?

70.One of the tallest candles ever constructed was exhibited at the 1897 Stockholm Exhibition.

If it cast a shadow 5 ft long at the same time a vertical pole 32 ft high cast a shadow 2 ft

long, how tall was the candle?

The Consumer Price Index (CPI) provides a means of

determining the purchasing power of the U.S. dollar from

one year to the next. Using the period from 1982 to 1984

as a measure of 100.0,the CPI for selected years from

1995 through 2007 is shown in the table. To use the CPI to

predict a price in a particular year, we set up a proportion

and compare it with a known price in another year:

Use the CPI figures in the table to find the amount that would be charged for using the same

amount of electricity that cost $225in 1995. Give your answer to the nearest dollar.

71.in 1997 72.in 1999 73.in 2003 74.in 2007

Convert each percent to a decimal. See Examples 7(a) and 7(b).

75.53% 76.38% 77.96% 78.11%

79.9% 80.7% 81.129% 82.174%

price in year A

index in year A

=

price in year B

index in year B

.

6

4

=

3

2

.

4.5

3

=

3

2

,

3

2

=

3

2

,

3

2

138 CHAPTER 2 Linear Equations and Inequalities in One Variable

x y

15

812

17

6

2

y 3

x

4

3

12

9

15

5

x

3

x

(^1212)
2
3 3
3
(^3322)
x
4
8
3
66
x
Year Consumer Price Index
1995 152.4
1997 160.5
1999 166.6
2001 177.1
2003 184.0
2005 195.3
2007 207.3
Source: Bureau of Labor Statistics.
(^24)
3
3
6
4.5
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