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Video: Finding the Drawing Scales given the Lengths in Real and in Drawing

Bethani Gasparine

A line on a drawing is 3 cm long. In real life, the object represented is 73.5 km long. What is the drawing scale?

01:30

Video Transcript

A line on a drawing is three centimeters long. In real life, the object represented is 73.5 kilometers long. What is the drawing scale?

A drawing scale is a way of comparing the length in the drawing to the length in the reality. The length in the drawing was three centimeters. And the length in reality was 73.5 kilometers. A scale should always be reduced. And both numbers can be divisible by three. So they can be reduced by three.

So this means, for every one centimeter in the drawing, it represents 24.5 kilometers in reality. So this means one centimeter in a drawing represents 24.5 kilometers in real life.

Now to get rid of our units, we need to multiply by the relationship between centimeters and kilometers. And for the units to cancel, we need kilometers on the numerator and centimeters on the denominator. And it is known that, in one kilometer, there are 100000 centimeters.

So now when multiplying, the kilometers cancel and the centimeters cancel. So on the numerator, we have one times one, which is one, and then 24.5 times 100000, which is equal to 2450000. It’s common to write a drawing scale using a colon. So our drawing scale will be one to 2450000.