# Scale

Scale is an expression synonymous with the word ratio.

Questions about scale deal with the relationship between the actual dimensions of an object and those of the drawing that represents it.

On the left appears the dimension of the graphical representation or map

On the right appears the real dimension.

Hint:

How can you remember that on the left you always see the scale of the scheme or drawing?

In the word left and in the word scale the letter $e$ appears.

Note: When writing scales, we must use the same units of measure in the scheme and in the real world.

If you have, for example, a dimension given in centimeters in the scheme and in reality it is in meters, the units must be converted so that they are identical and only then noted on the scale.

## Let's look at an example

The height of the building where Noa lives is $150$ meters.

Diana drew it on a sheet with a height of $50$ centimeters.

What is the scale?

Solution:

First, we will convert the units from reality (meters) to those of the drawing (centimeters).

$1$ meter is $100$ centimeters, therefore $15$ meters are $15,000$ centimeters.

Then we will note the scale according to the known standard, on the left side the measurements of the drawing and it will look like this:

$50:15,000$

## Let's look at another example

In the following map the given scale is $1:400$.
The distance on the map is $3$ cm.

What is the distance in reality?

Let's review what we have already learned, remember that, on the left side appears the number that represents the scheme and, on the right side the real dimension. That is, $1$ represents the scheme and $400$ represents reality.
Therefore, the real distance is $400$ times greater than the schematized one.
From the above it follows that the distance in the scheme is $3$ cm, therefore, in reality it is $1200$ cm or $12$ meters.

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