Scale Drawings

Since it is not always possible to draw on paper the actual size of real-life objects such as the real size of a car, an aeroplane, we need scale drawings to represent the size like the one you see below of a van.

In real life, the length of this van may measure 240 cm. However, the length of a copy or print paper that you could use to draw this van is a little bit less than 12 cm. Since 240/12 = 20, you will need about 20 sheets of copy paper to draw the length of the actual size of the van.

In order to use just one sheet, you could then use 1 cm on your drawing to represent 20 cm on the real-life object.

You can write this situation as 1:20 or 1/20 or 1 to 20.

Notice that the first number always refers to the length of the drawing on paper and the second number refers to the length of a real-life object.

Example 1:

Suppose a problem tells you that the length of a vehicle is drawn to scale. The scale of the drawing is 1:20.

If the length of the drawing of the vehicle on paper is 12 cm, how long is the vehicle in real life?

Set up a proportion that will look like this:

Do a cross product by multiplying the numerator of one fraction by the denominator of the other fraction.

We get :

Length of drawing × 20 = Real length × 1

Since length of drawing = 12, we get:

12 × 20 = Real length × 1

240 cm = Real length

Example 2:

The scale drawing of this tree is 1:500.

If the height of the tree on paper is 20 inches, what is the height of the tree in real life?

Set up a proportion like this:

Do a cross product by multiplying the numerator of one fraction by the denominator of the other fraction.

We get :

Height of drawing × 500 = Real height × 1

Since height of drawing = 20, we get:

20 × 500 = Real length × 1

10000 inches = Real height