Measurement is related to ratio and proportion in real life in many ways. Here are three types of examples:
First consider conversions. In one example if you compare inches to feet you are looking at a 12:1 ratio and you could solve for the length in feet of an 18 inch model using a proportion 12/1 = 18/x
In my favorite example changes in temperature are proportional at the rate of 5°C increase for every 9°F.
Secondly consider rates, a special type of ratio, often have to do with measurement Miles/hr, Dollars/ft², Miles/gallon
Thirdly there are special cases like scale models, maps, and similar figures where a scale factor exists between proportional objects.