finding quadratic eqaution from a word problem

michaela_mooney17 · #1 Nov 26, 2006, 09:59 AM

A farmer uses 400m of fencing to create a rectangular pig pen and to divide it into four equal regions. Algebraically determine the fucntion which gives the area of the pig pen as a function of its width, and state the dimensions that produce maximum area.

how do i start this off .. can anyone help me ?

asterisk_man · Nov 27, 2006, 10:30 AM

Start off by drawing a picture:

Code:

  <----w---->
/\+----+----+
| |    |    |
| |    |    |
h +----+----+
| |    |    |
| |    |    |
\/+----+----+

Now write an equation for the length of fence used:
3*w+3*h=400

Now write an equation for the area of the pen:
A=w*h

Solve the first equation for h so we can substitute it into the second (since the problem wants the equation in terms of w only).

3w+3h=400
3h=400-3w
h=400/3 - w

Substitute this into the second equation:

A=w*h
A=w*(400/3 - w)
A=(400w/3)-w^2

From here you should be able to solve for the width that gives the max area.



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