Warm Up
Solve each proportion.
6 = 2.4
1. 3 = x x = 45
2.
5
75
3. 9 = x
27
6
x
x=2
8
4. x = 8
3.5
7
x = 20
x=4
Vocabulary
Scale
Scale drawing
Scale model
Scale factor
Indirect Measurement
A scale gives the ratio of the dimensions in
the drawing to the dimensions of the object.
All dimensions are reduced or enlarged
using the same scale. Scales can use the
same units or different units.
A scale drawing is a two-dimensional
drawing of an object that is proportional
to the object.
A scale model is a three-dimensional
model that is proportional to the object.
Class Example
Under a 1000:1 microscope view, an amoeba
appears to have a length of 8 mm. What is its
actual length?
Write a proportion using the
1000 = 8 mm
scale. Let x be the actual
1
x mm
length of the amoeba.
1000

x=1

8
x = 0.008
The cross products are equal.
Solve the proportion.
The actual length of the amoeba is eight
thousandths of a millimeter.
Partner Practice
Under a 10,000:1 microscope view, a fiber
appears to have length of 1 mm. What is its
actual length?
10,000 = 1 mm
1
x mm
10,000

x=1

1
x = 0.0001
Write a proportion using the
scale. Let x be the actual
length of the fiber.
The cross products are equal.
Solve the proportion.
The actual length of the fiber is 1 tenthousandths of a millimeter.
Reading Math
The scale a:b is read “a to b.” For example,
the scale 1 cm:4 m is read “one centimeter
to four meters.”
Scale factor is the ratio of a length on a
scale drawing or model to the
corresponding length on the actual object.
When finding a scale factor, you must use
the same measurement units. You can use
a scale factor to find unknown dimensions.
Class Practice
The length of an object on a scale drawing is
4 cm, and its actual length is 12 m. The scale
is 1 cm: __ m. What is the scale?
1 cm = 4 cm Set up proportion using scale length .
xm
12 m
actual length
1  12 = x  4 Find the cross products.
12 = 4x
3=x
Divide both sides by 4.
The scale is 1 cm:3 m.
Partner Practice
A model of a 27 ft tall house was made using a
scale of 2 in.:3 ft. What is the height of the model?
2 in. = 2 in. = 1 in. = 1
Find the scale factor.
3 ft
36 in. 18 in. 18 Convert to same measurements
1 . Now set up a
The scale factor for the model is 18
proportion.
LetWhat
h equal
is “h”???
the height of the model.
1 = h in.
Convert: 27 ft = 324 in.
18 324 in.
324 = 18h
Find the cross products.
18 = h
Divide both sides by 18.
The height of the model is 18 in.
Individual Practice
A DNA model was built using the scale 5 cm:
0.0000001 mm. If the model of the DNA chain
is 20 cm long, what is the length of the actual
chain?
Find the scale factor.
5 cm
50 mm
=
0.0000001 mm
0.0000001 mm = 500,000,000
The scale factor for the model is 500,000,000.
This means the model is 500 million times larger
than the actual chain.
Individual Practice...continued
500,000,000 = 20 cm
1
x cm
500,000,000x = 1(20)
Set up a proportion.
Find the cross products.
Divide both sides by
x = 0.00000004 500,000,000.
The length of the DNA chain is 4  10-8 cm.
How is scale different than rate?
Discuss with your partner

Write an answer (in words)

Sometimes, distances cannot be measured
directly. One way to find such a distance is
to use indirect measurement, a way of
using similar figures and proportions to find
a measure.
Class Practice
Triangles ABC and EFG are similar. Find the
length of side EG.
AB = EF
Set up a proportion.
B
AC
EG
3 ft
A
C
4 ft
F
9 ft
E
x
3 9
=
4 x
Substitute 3 for AB, 4
for AC, 9 for EF, and x
for EG.
3x = 36
Find the cross products.
3x = 36
3
3
Divide both sides by 3.
x = 12
Divide both sides by 3.
G
The length of side EG is 12 ft.
Individual Practice
Triangles DEF and GHI are similar. Find the
length of side HI.
E
DE
GH
7 in
=
Set up a proportion.
2 in
EF
HI
D
H
F
x
8 in
G
2x = 56
Substitute values
for DE, EF, GH,
and HI.
2x = 56
2
2
x = 28
Find the cross
products and solve
for x.
2 = 8
7
x
I
The length of side HI is 28 in.