1. Scale Drawings & Models
What you will learn:
Use scale drawings
Construct scale drawings

2. Vocabulary
Scale drawing/scale model: is used to represent an object that is too large or too small to be drawn or built at actual sizes
Scale: gives the relationship between the measurements on the drawing or model and the measurements of the real object
Scale factor: the ratio of a length on a scale drawing or model to the corresponding length on the real object

3. Scale Example: 1 inch = 3 feet 1:24
(One inch represents an actual distance of 3 feet)
1:24
(1 unit represents an actual distance of 24 units)

4. Scale Factor
Example: Suppose a scale model has a scale of 2 inches = 16 inches. The scale factor is 2 or 8
The lengths and widths of objects of a scale drawing or model are proportional to the lengths and widths of the actual object.

5. Find Measurements
Landscape plans shows a flower bed that is 6.5 inches wide. The scale on the plans is 1 inch = 4’
Q: What is the width of the actual flower bed?
Let x represent the actual width of the flower bed.
Write and solve a proportion.
Plan width----> 1 inch = 6.5 inches
Actual width--> 4 feet x feet
1  x = 4  {cross multiply!}
x= 26
The actual flower bed width is 26 feet.

6. From the last example, what is the scale factor?
To find the scale factor, write the ratio of 1 inch to 4 feet in simplest form.
1inch = 1 inch
4 feet inches {Convert 4’ to inches}
The scale factor is 1/48 . That is , each measurement on the plan is 1/48th of the actual measurement.

7. Determine the Scale Model height---> 6 inches = 1 inch
Q: In a scale model of a roller coaster, the highest hill has a height of 6 inches. If the actual height of the hill is 210 feet, what is the scale of the model?
Model height---> 6 inches = 1 inch
Actual height--->210 feet x feet
6x = 210
6x = x= 35
So, the scale is 1” = 35 feet

8. Construct a Scale Drawing
Q: A garden is 8 feet wide by 16 feet long. Make a scale drawing of the garden that has a scale of 1 in. = 2ft. 4
Step 1: Find the measure of the garden’s length on the drawing. Let x represent the length.
drawing length--> .25in = x in
actual length--> ft 16ft
.25  16 =2  x
4 = 2x
2 = x
On the drawing, the length is 2 inches

9. Construct a Scale Drawing
Step 2: Find the measure of the garden’s width on the drawing. Let w represent the width.
drawing width--> .25 in = w inches
actual width ---> 2 feet feet
.25  8 = 2  w
2 = 2w
1 = w
On the drawing the width is 1 inch.