# Thread: Need help with this word problem. finding the function

1. ## Need help with this word problem. finding the function

A rancher with 750ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle.

a. Find a function that models the total area of the four pens.

b. Find the largest possible total area of the four pens.

ok so I am not sure where to even start with questions a or b.
I am thinking with part a I need to find the area of the rectangle?
5W+2L+750 ? then what?

If someone could explain to me step by step so I can understand it please and thank you in advanced.

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Originally Posted by allabouttheb's
A rancher with 750ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle.

a. Find a function that models the total area of the four pens.

b. Find the largest possible total area of the four pens.

ok so I am not sure where to even start with questions a or b.
I am thinking with part a I need to find the area of the rectangle?
5W+2L+750 ? then what?

If someone could explain to me step by step so I can understand it please and thank you in advanced.
The interior fencing is parallel to one side of the rectangle, so let's suppose that the length of each of these interior fences - as well as the two exterior fences that are parallel to them - is $x$ feet. Then these 5 fences take $5x$ feet of fencing altogether.

There are then $(750 - 5x)$ feet of fencing remaining, that must be divided equally to form the other two sides of the rectangle. So that's $\tfrac12(750-5x)$ feet for each side.

So the whole enclosure measures $x$ feet by $\tfrac12(750-5x)$ feet, or $\tfrac12x(750-5x)$ square feet in area. There's our function, then, for part (a):

$A = \tfrac12x(750-5x)$

This is a quadratic expression in $x$. I assume you've been shown a method to find its maximum value. So can you complete part (b) now?

3. So would
A=375x-2.5x^2
?

4. Originally Posted by allabouttheb's
So would
A=375x-2.5x^2
?
Yes. Can you find its maximum value?