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/