Scale

The following is a picture of an airplane:

Obviously, this picture is NOT drawn real size. (We would need a REALLY big piece of paper to draw that!) But this picture IS drawn to scale - that means that it looks exactly like the real plane - but every piece is smaller. What you are going to learn is how to use scale to state how wide and long this plane is in real life.

Example 1

Using the scale drawing of the plane above, state it's actual width and length, if the scale being used is 1:50.

Solution

The first thing to examine is the scale itself. The question states that the scale is 1:50. This means that every 1 scale unit shown on the diagram equals 50 real-life units. Note that this scale does not involve specific units. 1 cm on the picture would be 50 cm in real life. 1 inch on the picture would be 50 inches in real life. Since the diagram above is already measured in inches, we will work in inches.

To solve a scale problem, it is usually best to use a proportion. For help on proportions, check out the proportions section of Unit 1 of this course.

To set up this proportion, write the scale on the left hand side of the proportion:

Notice that we have labelled the 'top' of the proportion scale and the 'bottom' of the proportion real. Scale is ALWAYS set up this way:

scale units:real units OR scale units/real units.

Let's work on the width first. In the diagram, the width is shown to be 4.2 inches. This is the scale measurement. Place this into the proportion on the top, since the top represents the scale dimensions. You should be looking at the following:

Now cross-multiply and divide to arrive at an answer:

x = 50(4.2) / 1
x = 210"

So we know that the actual life-size width of the plane is 210". Follow the same series of steps to find the length of the airplane:

x = 50(3.9) / 1
x = 195"

Now we know that the plane is 210" by 195" or (dividing both by 12 since 12" = 1') we get 17.5' by 16.25'.

Example 2

How high would you have to draw the empire state building on a page to scale if the Empire State Building is 1250 ft and you are using a scale of 1 cm : 50 ft?

Solution

There are two differences between this example and the previous example. The first difference is that we are working from life - size TO scale size. The second is that the scale has specified units. Neither of these changes has a huge effect on how we find the solution.

First, set up another proportion using your scale. It should look like the following:

Since you are given the real size of the Empire State Building in the question, you will put this value on the 'bottom' of the left hand side of the proportion. Your solution should look like the following:

x = 1250(1) / 50
x = 25

Therefore, the scale height of the building should be 25 cm.

These are the only types of questions that you will encounter when working with scale: Changing from scale to life-size and from life-size back to scale size. Once you have familiarized yourself with these examples, you can try the exercises in your booklet and you can head back to the Design and Measurement main page.