# Word problem help

#### thetomps

##### Junior Member
I am trying to help my sister who is stuck on this problem for her alegbra class. Can someone show me how to do it so I know what I am talking about when I try to explain this to her. Thanks.

Kay Thompson

A rancher has 20 miles of fencing to fence a rectangular piece of grazing land along a straight river. If no fence is required along the river and the sides perpendicular to the river are x miles long, find a formula for the area A(x) of the rectangle in terms of x. From practical considerations, what is the domain of the function A?

Thanks again!

Staff member

#### Gene

##### Senior Member
Since the blind are leading the blind, what Elizh said in
http://www.freemathhelp.com/forum/posti ... st&p=30067
was
20=w+2x
w=20-2x
'cause you have 20 mi and 2 x long pieces from the river.
A= wx
A=f(x) = (20-2x)*x =
20x-2x^2
We can't ask her what she knows about downward opening parabolas so I have to guess. The vertex of ax^2+bx is at
-b/2a = -20/(2*-2) = 5
so the maximum area is when x=5. If she uses some other way to find the vertex, it is still at x=5
w=20-2x=10
A=wx=50 sq miles.
w=20-2*5=10
Do not double post!!