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### Dimensions of a Rectangle

```
Date: 8/26/96 at 0:14:47
From: Anonymous
Subject: Area of a Rectangle

A rectangle is three times as long as it is wide.  If its length and
width are both increased by 3 m, its area is increased by 81 m
squared.  Find its original dimensions.

I understand that the width would be labeled "w", and each length
would be labeled "3w".
```

```
Date: 8/30/96 at 13:0:41
From: Doctor Jerry
Subject: Re: Area of a Rectangle

Good first step! The next step is to use w and 3w in expressing the
given sentences as equations.  For example, if length and width are
both increased by 3 meters, then the new length and width are w+3 and
3w+3.

Further, since the area is increased by 81 meters, the new area minus
the old area is 81.  The old area is w*(3w); the new area is

(w+3)*(3w+3).

Putting all of this together,

(w+3)*(3w+3)-w*(3w)=81.

After simplifying this equation you will find that w = 6.

Does this fit?  Well, original rectangle is 6 by 18, with area 108.
If length and width are increased by 3, new rectangle is 9 by 21.  The
area of new rectangle is 189.  189-108 = 81.  Everything checks.

-Doctor Jerry,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Algebra
Middle School Geometry
Middle School Triangles and Other Polygons

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