Using Scale Drawings

Date: 05/24/2002 at 18:26:55
From: Laura Saylor
Subject: Scale drawings

How do I do scale drawings?  For example, if the scale is 3 cm = 5 m, 
and the drawing is a Bairds Whale, how do I do it?  My math book does 
not really help.  Maybe you could?

Date: 05/24/2002 at 22:36:39
From: Doctor Peterson
Subject: Re: Scale drawings

Hi, Laura.

You haven't quite said what you have to do with the scale drawing. In 
this case, it sounds like you are given the drawing and have to 
determine how big the real whale is.

One thing you might like to do is to just play with this drawing a 
bit to get a feel for how it works. You can make a ruler to work with 
the drawing, by taking a strip of paper and making a mark every 3 
centimeters along the edge. Label the first mark "0 m", the next "5 
m", the next "10 m", and so on. That's because you are told that 3 cm 
on the drawing stands for 5 m in real life. Once you've made this 
scale ruler, you can just measure the whale with it!

Now think about how you could avoid that extra work. If you just 
measured the drawing with a regular ruler, and found that it was, 
say, 15 cm long, what would your scale ruler say? If you divide 15 by 
3, you find that there would have been 5 of your 3 cm divisions. 
Since each of those stands for 5 meters, the whale is 5 times 5 
meters long, or 25 meters.

I think if you try first using, and then imagining, rulers like this, 
you will be able to find your own way to solve each problem. You may 
be taught quicker ways, and you'll want to see how those compare to 
the ways you figure out for yourself, and why they work. But make 
sure you understand how things work before you just take a "rule" and 
try to follow it.

If you need more specific help, feel free to tell me some particular 
problems you have, and where you get stuck doing them.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/