5-8 Scale Drawings and Scale Models
Holt CA Course 1
5-8 Scale Drawings and Scale Models
Holt CA Course 1
5-8 Scale Drawings and Scale Models
Holt CA Course 1
5-8 Scale Drawings and Scale Models
Holt CA Course 1
5-8 Scale Drawings and Scale Models
Holt CA Course 1
5-8 Scale Drawings and Scale Models
Preview
Warm Up
California Standards
Lesson Presentation
Holt CA Course 1
5-8 Scale Drawings and Scale Models
Warm Up
Write each fraction in simplest form.
4 1 2. 9 1
1. 15
48 12 135
Convert the following measurements.
3. 192 inches = feet 16
4. 18.5 feet = inches 222
5. 324 inches = feet 27
Holt CA Course 1
5-8 Scale Drawings and Scale Models
California
Standards
NS1.3 - Use proportions to solve
problems (e.g., determine the value of
N if 4 = N , find the length of a side of a
7 21
polygon similar to a known polygon). Use
cross-multiplication as a method for solving
such problems, understanding it as the
multiplication of both sides of an equation by a
multiplicative inverse.
Holt CA Course 1
5-8 Scale Drawings and Scale Models
Objective: You will learn how to
understand ratios and proportions in
scale drawings and use ratios and
proportions with scale.
Holt CA Course 1
5-8 Scale Drawings and Scale Models
Vocabulary
scale model
scale factor
scale
scale drawing
Holt CA Course 1
5-8 Scale Drawings and Scale Models
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
1
gauge model train is .
87
This means that each dimension of the model is 1 of
the corresponding dimension of the actual 87
train.
Holt CA Course 1
5-8 Scale Drawings and Scale Models
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 two-dimensional
drawing of an object. Both scale drawings and scale
models can be smaller or larger than the objects
they represent.
Holt CA Course 1
5-8 Scale Drawings and Scale Models
Example 1: Finding a Scale Factor
Identify the scale factor.
You can use the Room Blueprint
lengths or widths to Length (in.) 144 18
find the scale factor. Width (in.) 108 13.5
blueprint length = 18 = 1 Write a ratio.
room length 144 8 Then simplify.
blueprint width = 13.5 = 1 Write a ratio.
room width 108 8 Then simplify.
1
The scale factor is .
8
Holt CA Course 1
5-8 Scale Drawings and Scale Models
Check It Out! Example 2
Identify the scale factor.
Model Aircraft Blueprint
Length (in.) 12 2
Wing span (in.) 18 3
blueprint length = 2
= 1 Then simplify.
Write a ratio.
aircraft length 12 6
blueprint wing span = 3
= 1 Then simplify.
Write a ratio.
aircraft wing span 18 6
1
The scale factor is .
6
Holt CA Course 1
5-8 Scale Drawings and Scale Models
Example 3: Using Scale Factors to Find Unknown Lengths
A photograph was enlarged and made into a poster. The
poster is 20.5 inches by 36 inches.
5
The scale factor is 1. Find the size of the original
photograph to the nearest tenth of an inch.
Think: poster = 5
photo 1
36 = 5 Write a proportion
to find the length l.
l 1
Find the cross
5l = 36 products.
l = 7.2 Divide.
Holt CA Course 1
5-8 Scale Drawings and Scale Models
Example 3 Continued
A photograph was enlarged and made into a poster. The
poster is 20.5 inches by 36 inches.
The scale factor is 5 . Find the size of the photograph.
1
Think: poster = 5
photo 1
20.5 = 5 Write a proportion to
w find the width w.
1
Find the cross
5w = 20.5 products.
w = 4.1 Divide.
The photo is 7.2 in. long and 4.1 in. wide.
Holt CA Course 1
5-8 Scale Drawings and Scale Models
Check It Out! Example 4
Mary’s father made her a dollhouse which was modeled
after the blueprint of their home. The blueprint is 24
inches by 45 inches. The scale
factor is 1.5 . Find the size of the dollhouse.
1
dollhouse = 1.5
Think:
blueprint 1
l = 1.5 Write a proportion to
1 find the length l.
45
l = 45 · 1.5 Find the cross
products.
l = 67.5 Multiply.
Holt CA Course 1
5-8 Scale Drawings and Scale Models
Check It Out! Example 4 Continued
Mary’s father made her a dollhouse which was modeled
after the blueprint of their home. The blueprint is 24
inches by 45 inches. The scale
1.5
factor is . Find the size of the dollhouse.
1
Think: dollhouse = 1.5
blueprint 1
w = 1.5 Write a proportion
24 1 to find the width w.
Find the cross
w = 24 · 1.5 products.
w = 36 Multiply.
The dollhouse is 67.5 inches long and 36 inches wide.
Holt CA Course 1
5-8 Scale Drawings and Scale Models
Example 5: Measurement Application
On a road map with a scale of 1.5 inches = 60 miles, the
distance between Pittsburgh and Philadelphia is 7.5 inches.
What is the actual distance between the cities?
Let d be the actual distance between the cities.
1.5 = 7.5 Write a proportion.
60 d
1.5 · d = 60 · 7.5 Find the cross product.
1.5d = 450 Multiply.
1.5d = 450 Divide both
1.5 1.5 sides by 1.5
d = 300
The distance between the cities is 300 miles.
Holt CA Course 1
5-8 Scale Drawings and Scale Models
Check It Out! Example 6
On a road map with a scale of 1 inch = 50
kilometers, the distance between Dallas and Houston
is 7 inches. What is the actual distance between the
two cities?
Let d be the actual distance between the cities.
1= 7
Write a proportion.
50 d
1 · d = 50 · 7 Find the cross products.
1d = 350 Multiply.
d = 350
The distance between the cities is 350 kilometers.
Holt CA Course 1
5-8 Scale Drawings and Scale Models
Holt CA Course 1
5-8 Scale Drawings and Scale Models
Lesson Quiz
Identify the scale factor.
1. Statue of Liberty Model
1
Height
(in.)
1,824 8 228
2. On a scale drawing, a kitchen wall is 6 inches long.
1
The scale factor is 24. What is the length of the
actual wall? 144 inches, or 12 feet
3. On a road map, the distance from Green Bay to
Chicago is 11 cm. What is the actual distance
between the cities if the map scale is 3 cm = 90 km?
330 km
Holt CA Course 1
5-8 Scale Drawings and Scale Models
Holt CA Course 1
5-8 Scale Drawings and Scale Models
Holt CA Course 1
5-8 Scale Drawings and Scale Models
Holt CA Course 1
5-8 Scale Drawings and Scale Models
Holt CA Course 1
5-8 Scale Drawings and Scale Models
Holt CA Course 1
5-8 Scale Drawings and Scale Models
Holt CA Course 1
5-8 Scale Drawings and Scale Models
Holt CA Course 1
5-8 Scale Drawings and Scale Models
Holt CA Course 1