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Maths Exercices

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.

Susan is driving to Mount Shasta. On her map, she is a distance of 7 inches away. The scale of the map is 4 inch = 212 miles. How far must Susan travel to reach her destination?

Susan must travel milles