1. 7-7 Scale Drawings
7-7 Scale Drawings
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
Pre-Algebra
2. 7-7 Scale Drawings
Warm Up
Evaluate the following for x = 16.
1. 3x 48 2. 3 x 12
4
Evaluate the following for x = 2.
5
1
3. 10x 4 4. 1x
4 10
Pre-Algebra
3. 7-7 Scale Drawings
Problem of the Day
An isosceles triangle with a base length
of 6 cm and side lengths of 5 cm is
dilated by a scale factor of 3. What is
the area of the image?
108 cm2
Pre-Algebra
4. 7-7 Scale Drawings
Learn to make comparisons between and
find dimensions of scale drawings and
actual objects.
Pre-Algebra
6. 7-7 Scale Drawings
A scale drawing is a two-dimensional
drawing that accurately represents an
object. The scale drawing is
mathematically similar to the object.
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.
Pre-Algebra
7. 7-7 Scale Drawings
Scale Interpretation
1:20 1 unit on the drawing is 20 units.
1 cm: 1 m 1 cm on the drawing is 1 m.
1 1
4 in. = 1 ft 4
in. on the drawing is 1 ft.
Reading Math
The scale a:b is read “a to b.” For example,
the scale 1 cm:3 ft is read “one centimeter
to three feet.”
Pre-Algebra
8. 7-7 Scale Drawings
Additional Example 1A: Using Proportions to Find
Unknown Scales or Lengths
A. The length of an object on a scale drawing
is 2 cm, and its actual length is 8 m. The
scale is 1 cm: __ m. What is the scale?
1 cm = 2 cm Set up proportion using scale length .
xm 8m actual length
1 8 = x 2 Find the cross products.
8 = 2x
4=x Solve the proportion.
The scale is 1 cm:4 m.
Pre-Algebra
9. 7-7 Scale Drawings
Additional Example 1B: Using Proportions to Find
Unknown Scales or Lengths
B. The length of an object on a scale drawing
is 1.5 inches. The scale is 1 in:6 ft. What is
the actual length of the object?
1 in. = 1.5 in. Set up proportion using scale length .
6 ft x ft actual length
1 x = 6 1.5 Find the cross products.
x=9 Solve the proportion.
The actual length is 9 ft.
Pre-Algebra
10. 7-7 Scale Drawings
Try This: Example 1A
A. 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 Solve the proportion.
The scale is 1 cm:3 m.
Pre-Algebra
11. 7-7 Scale Drawings
Try This: Example 1B
B. The length of an object on a scale drawing
is 2 inches. The scale is 1 in:4 ft. What is
the actual length of the object?
1 in. = 2 in. Set up proportion using scale length .
4 ft x ft actual length
1 x = 4 2 Find the cross products.
x=8 Solve the proportion.
The actual length is 8 ft.
Pre-Algebra
12. 7-7 Scale Drawings
A scale drawing that is smaller than the
actual object is called a reduction. A
scale drawing can also be larger than the
object. In this case, the drawing is
referred to as an enlargement.
Pre-Algebra
13. 7-7 Scale Drawings
Additional Example 2: Life Sciences Application
Under a 1000:1 microscope view, an amoeba
appears to have a length of 8 mm. What is its
actual length?
1000 = 8 mm scale length
1 x mm actual length
1000
x=1
8 Find the cross products.
x = 0.008 Solve the proportion.
The actual length of the amoeba is 0.008 mm.
Pre-Algebra
14. 7-7 Scale Drawings
Try This: Example 2
Under a 10,000:1 microscope view, a fiber
appears to have length of 1mm. What is its
actual length?
10,000 = 1 mm scale length
1 x mm actual length
10,000
x=1
1 Find the cross products.
x = 0.0001 Solve the proportion.
The actual length of the fiber is 0.0001 mm.
Pre-Algebra
15. 7-7 Scale Drawings
1
A drawing that uses the scale 4 in. = 1 ft
1
is said to be in 4 in. scale. Similarly, a
1
drawing that uses the scale 2 in. = 1 ft is
1
in 2 in. scale.
Pre-Algebra
16. 7-7 Scale Drawings
Additional Example 3A: Using Scales and Scale
Drawings to Find Heights
A. If a wall in a 1 in. scale drawing is 4 in. tall,
4
how tall is the actual wall?
0.25 in. = 4 in. scale length Length ratios are
1 ft x ft. actual length equal.
0.25
x=1
4 Find the cross
products.
x = 16 Solve the
proportion.
The wall is 16 ft tall.
Pre-Algebra
17. 7-7 Scale Drawings
Additional Example 3B: Using Scales and Scale
Drawings to Find Heights
B. How tall is the wall if a 1 in. scale is used?
2
0.5 in. = 4 in. scale length Length ratios are
1 ft x ft. actual length equal.
0.5
x=1
4 Find the cross
products.
x=8 Solve the
proportion.
The wall is 8 ft tall.
Pre-Algebra
18. 7-7 Scale Drawings
Try This: Example 3A
A. If a wall in a 1 in. scale drawing is 0.5 in.
4
thick, how thick is the actual wall?
0.25 in. = 0.5 in. scale length Length ratios are
1 ft x ft. actual length equal.
0.25
x=1
0.5 Find the cross
products.
x=2 Solve the
proportion.
The wall is 2 ft thick.
Pre-Algebra
19. 7-7 Scale Drawings
Try This: Example 3A Continued
B. How thick is the wall if a 1 in. scale is used?
2
0.5 in. = 0.5 in. scale length Length ratios are
1 ft x ft. actual length equal.
0.5
x=1
0.5 Find the cross
products.
x=1 Solve the
proportion.
The wall is 1 ft thick.
Pre-Algebra
20. 7-7 Scale Drawings
Lesson Quiz
1. What is the scale of a drawing in which a 9 ft
wall is 6 cm long? 1 cm = 1.5 ft
2. Using a 1in. = 1 ft scale, how long would a
4
drawing of a 22 ft car be? 5.5 in.
3. The height of a person on a scale drawing is
4.5 in. The scale is 1:16. What is the actual
height of the person? 72 in.
The scale of a map is 1 in. = 21 mi. Find each
length on the map.
4. 147 mi 7 in. 5. 5.25 mi 0.25 in.
Pre-Algebra
