Width and Area of a Field

Date: 8/22/96 at 22:31:15
From: Anonymous
Subject: Quadratic Equation Word Problem

The question is:

A farmer has a 300 ft of fencing and wants to enclose a rectangular 
field. Find a quadratic equation that relates the area of the field to 
its width.

Date: 8/23/96 at 0:24:40
From: Doctor Paul
Subject:  Quadratic Equation Word Problem

We know that Length * Width = Area and that 2*L + 2*W = 300.

Solve the second equation for L:

2L = 300 - 2W
 L = 150 - W

and substitute that equation for L into the first equation:

(150 - W) * W =  A

   150W - W^2 =  A

That, my friend, is an equation that relates the area of the field to 
its width.  I hope this clears things up.

Regards,
-Doctor Paul,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/