# 5-7 Scale Drawings and Scale Models.ppt

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```					 5-7 Scale Drawings and Scale Models

Course 2
5-7 Scale Drawings and Scale Models

Warm Up
Write each fraction in the 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

Course 2
5-7 Scale Models and Scale Drawings

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 .
1
This means that each dimension of the model is
87
of the corresponding dimension of the actual train.

Course 2
5-7 Scale Models and Scale Drawings

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.

Course 2
5-7 Scale Drawings and Scale Models

Example 1: Finding a Scale Factor

Identify the scale factor.

Room   Blueprint
Length (in.)     144          18
Width (in.)      108      13.5

blueprint length = 18       Write a ratio using one of the
room length       144     dimensions.
= 1        Simplify.
8
The scale factor is 1 .
8
Course 2
5-7 Insert Drawings and Scale Models
Scale Lesson Title Here
Try This: Example 1

Identify the scale factor.

Model Aircraft     Blueprint
Length (in.)           12                2
Wing span (in.)              18                3

blueprint length = 2           Write a ratio using one of
aircraft length     12        the dimensions.
= 1          Simplify.
6
The scale factor is 1 .
6
Course 2
5-7 Scale Drawings and Scale Models
Example 2: 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. The scale
5
factor is 1 . Find the size of the photograph.
poster = 5
Think:
photo     1
36 = 5       Write a proportion to find the
l   1       length l.

5l = 36   Find the cross products.

l = 7.2   Divide.

Course 2
5-7 Scale Drawings and Scale Models
Example 2 Continued

A photograph was enlarged and made into a poster.
The poster is 20.5 inches by 36 inches. The scale
5
factor is 1 . Find the size of the photograph.
poster = 5
Think:
photo     1
20.5 = 5      Write a proportion to find the
w     1      width w.

5w = 20.5 Find the cross products.
w = 4.1 Divide.
The photo is 7.2 in. long and 4.1 in. wide.
Course 2
5-7 Scale Drawings and Scale Models
Try This: Example 2

Katie’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
45    1         find the length l.
Find the cross
l = 45 · 1.5
products.
l = 67.5       Multiply.

Course 2
5-7 Scale Drawings and Scale Models
Try This: 2 Continued

Ariel’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
w = 1.5       Write a proportion
24   1        to find the width w.

w = 24 · 1.5 Find the cross products.
w = 36        Multiply.
The dollhouse is 67.5 inches long and 36 inches wide.
Course 2
5-7 Scale Drawings and Scale Models
Example 3: 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?
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 products.
1.5d = 450         Multiply.
1.5d = 450
Divide.
1.5    1.5
d = 300
The distance between the cities is 300 miles.
Course 2
5-7 Insert Drawings and Scale Models
Scale Lesson Title Here
Try This: Example 3
On a road map, the distance between Dallas
and Houston is 7 inches. What is the actual
distance between the cities if the map scale is
1 inch = 50 kilometers?
Let d be the actual distance between the cities.
1= 7
50 d
Write a proportion.
1 · d = 50 · 7           Find the cross products.
1d = 350               Multiply.
d = 350

The distance between the cities is 350 kilometers.

Course 2
5-7 Scale Drawings andHere Models
Insert Lesson Title Scale

Assignment:
pg. 290-291 1-13 All

Course 2

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