Scale drawings and scale factors
A scale drawing is a drawing of a real object in which all the dimensions are proportional to the real object. A scale drawing can be larger or smaller than the object it represents. The scale is the ratio of the drawing size to the actual size of the object.
- The ratio of the length of the scale drawing to the corresponding length of the actual object is called as scale factor.
- The ratio of any two corresponding lengths in two similar geometric figures is called as scale factor.
On a map having a scale of 1 inch = 25 miles, the distance between two cities is 3.2 inches. What is the actual distance between the two cities?
Let d = the actual distance between the cities. Write and solve a proportion. Use the scale written as a fraction.
1 × d = 25 × 3.2 Cross products
d = 80 Simplify.
The actual distance between the two cities is 80 miles.
Designers are creating a child-sized version of a doll’s dress. If they use a scale of 10 inches = 1 inch and the doll’s dress has a length of 4.5 inches, what is the length of the child-sized dress?
Write a proportion using the scale.
10 × 4.5 = 1 × c Find the cross products.
45 = c Multiply.
The child-sized dress is 45 inches long.
A die-cast model of a car was prepared using a scale of 2 inches : 3.4 meters. If the model measures 3 inches in length, then find the actual length of the car.
The actual length of the car is meters