1. Lesson 6.5 Scale Drawings
Students will be able to understand ratios and proportions in scale drawings.

2. Write each fraction in the simplest form.
Warm Up
Write each fraction in the simplest form. 4 48 1 12 1. 9
135 1 15
Convert the following measurements:
192 inches = ________ feet
18.5 feet = ________ inches
inches = ________ feet 16
222 27

3. This HO gauge model train is a scale model of a historic train
This HO gauge model train is a scale model of a historic train. A scale model is a proportional model of a three-dimensional object. Its dimensions are related to the dimensions of the actual object by a ratio called the scale factor. The scale factor of an HO
gauge model train is 1 87 1 87
This means that each dimension of the model is of the corresponding dimension of the actual train.
(1 inch on the model is 87 inches on the actual train.)

4. A scale is the ratio between two sets of measurements
A scale is the ratio between two sets of measurements. Scales can use the same units or different units. The photograph shows a scale drawing of the model train.
A scale drawing is a proportional drawing of an object. Both scale drawings and scale models can be smaller or larger than the objects they represent.

5. Write a ratio using one of the dimensions
Identify the scale factor.
Room
Blueprint
Length
12 ft.
18 in.
Width
9 ft.
13.5 in.
Write a ratio using one of the dimensions
Blueprint Length
Room Length
18 in.
12 ft. =
Units are like quantities (length to length). They must be converted to common units!
Which unit will you convert?
FEET to INCHES
12 ft x _____ 12 1
in. =
144 in.
Now replace 12ft with 144 in. 1
ft. 18 18
Simplify. (Scale factor ratios must be written as a single unit rate)
18 in.
144 in. =
Remember from lesson 6.1 when common units (in.) are used the ratio will NOT have units! 1 8
The scale factor is:

6. First: Write a ratio using one of the dimensions
Identify Scale Factor: Your Turn!
Room
Blueprint
Length
8 ft.
1 in.
Width
18 ft.
2.25 in.
First: Write a ratio using one of the dimensions
Blueprint width
Room width or
2.25 in.
18 ft.
Blueprint length
Room length
Units are like quantities (length to length). They must be converted to common units!
Which unit will you convert? or
Room width
Blueprint width
FEET to INCHES
18 ft. x _________ 12 1
in.
ft. =
216 in. 1
Simplify. (Scale factor ratios must be written as a single unit rate)
2.25 in.
216 in.
2.25 1 96 = 1 96
The scale factor is:

7. : : = = 300 = x Measurement Application
On a road map, the distance between Pittsburgh and Philadelphia is 7.5 inches. What is the actual distance between the cities if the map scale is 1.5 inches = 60 miles?
Write a proportion
Pittsburgh to Philadelphia (map)
Pittsburgh to Philadelphia (actual) =
Scale (map)
Scale (actual)
Substitute Values
7.5 in.
X miles =
1.5 in.
60 miles
Cross Products
7.5 x 60 = 1.5x : :
Divide Both sides by 1.5
450 = 1.5x
300 = x
The distance between the cities is 300 miles.

8. = = 2.5in. 3 in. 1 in. = 2 ft. = 1in scale 2ft scale
Use the scale on the drawing to find the scale factor and the perimeter of the tree house. 1 24
Convert to same units for scale factor.
1 in.
2ft.
In.
The scale is: = 1 24
2 ft. x 12 in.
ft. =
24 in
Scale factor =
Perimeter of
Drawing
Actual object
1in scale
2ft scale
Write a proportion to find the perimeter of the actual object. =
2.5in.
3 in.
11 in.
x ft.
1 in.
2 ft.
Substitute. =
1 in. = 2 ft.
Use cross products.
11 x 2 = 1x
22 = x
The actual perimeter of the tree house is 22 ft.

9. Homework Time:
Page 287 problems 1-16 all