Find the Perimeter

Date: 04/09/2002 at 14:12:13
From: Holly Ellebracht
Subject: Area and perimeter

I have a problem. I have a group of 13 rectangles arranged into a 
larger rectangle. I know the area, but I need to find the perimeter.  
How do I do this? The rectangles are arranged with eleven parallel in 
one row, and two that are sideways on the bottom. The area I'm given 
is 1144 squared.  
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The rectangles are all equal in shape, and I don't know how to find 
the perimeter. 

Thanks!
-Holly

Date: 04/09/2002 at 15:43:37
From: Doctor Ian
Subject: Re: Area and perimeter

Hi Holly,

Let's look at a smaller version, with three rectangles on top, and two 
on the bottom. 

            w
  +---+---+---+
  |   |   |   | h
  |   |   |   |
  +-----+-----+
  |     |     | w
  +-----+-----+
           h

What this picture tells us is that 3 times the width (w) of a single 
rectangle is equal to twice the height (h) of a single rectangle.  Do 
you see why?  

This means that

      3w = 2h

  (3/2)w = h

Now, what is the area of the whole thing? Again, the picture tells us 
that the width of the whole thing is 3w; and the height of the whole 
thing is (h+w). 

This means that 

  area = 3w(h+w)

But we know that h = (3/2)w, so 

  area = 3w((3/2)w + w)

       = 3w((5/2)w)

       = (15/2)w^2

So if I know the area, I can find w; and if I know w, I can find h. 

Can you apply the same reasoning to your problem? 

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