Associated Topics || Dr. Math Home || Search Dr. Math

### 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.
_________________________________
|  |  |  |  |  |  |  |  |  |  |  |
|  |  |  |  |  |  |  |  |  |  |  |
|  |  |  |  |  |  |  |  |  |  |  |
----------------------------------
|                 |
__________________________________

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/
```
Associated Topics:
High School Triangles and Other Polygons
Middle School Triangles and Other Polygons

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search