Question

How do scale drawings and actual measurements represent proportional relationship

Answer 1

Scale drawings is a ratio. For example: scale 1 cm : 100 km, represents the ratio

 1 cm
----------
100 km

The measure on the map, call it m, and the actual measure, call it x (the unknown) makes another ratio:

   m
-------
   x.

Those two ratios constitue a proportion or proportional relationship:

  1 cm          m
------------ = ------
 100 km        x

That proportion permits to find the actual measurement (x) from the measurement of the map (m).

Suppose you measure 4.5 cm on the map, then you calculate the actual measure as:

x = [ 100 km / 1 cm] * 4.5 cm = 450 km.

As you have seen, scale drawings and actual measurements represent a proportion which lets you to find the unknown.