Area problem, involving quadratic functions

[bonnieerika]

Hi, I don't understand what this question is asking and I have idea how to do it.. any help is very much appreciated! I understand how to complete the square, parabolas and such and the concept of maximum and minimum, I just don't understand this question.

A Cattle farmer wants to build a rectangular fenced enclosure divided into 5 rectangular pens. Each pen has equal area.

[diagram shows picture of 5 rectangular pens side by side, all of them are the same size]

A total length of 120 m of fencing material is available. Find the overall dimensions of the enclosure that will make the total area a maximum.

 

[Mentallic]

Hi, I don't understand what this question is asking and I have idea how to do it.. any help is very much appreciated! I understand how to complete the square, parabolas and such and the concept of maximum and minimum, I just don't understand this question.

A Cattle farmer wants to build a rectangular fenced enclosure divided into 5 rectangular pens. Each pen has equal area.

[diagram shows picture of 5 rectangular pens side by side, all of them are the same size]

A total length of 120 m of fencing material is available. Find the overall dimensions of the enclosure that will make the total area a maximum.

Start by drawing out the enclosure and labelling the dimensions of a single rectangle with x and y (or you can give the entire enclosure those variables if you wish).
Now, what is the area equal to in terms of x and y? i.e. Find A(x,y).
What about the length of fencing in terms of x and y? We also know that the fencing is 120m so you'll have an equation in two variables given by F(x,y)=120.

 

[Ray Vickson]

Hi, I don't understand what this question is asking and I have idea how to do it.. any help is very much appreciated! I understand how to complete the square, parabolas and such and the concept of maximum and minimum, I just don't understand this question.

A Cattle farmer wants to build a rectangular fenced enclosure divided into 5 rectangular pens. Each pen has equal area.

[diagram shows picture of 5 rectangular pens side by side, all of them are the same size]

A total length of 120 m of fencing material is available. Find the overall dimensions of the enclosure that will make the total area a maximum.

You really do need to make an effort before asking for help, but here are some hints.

Try drawing a couple of different "designs", each using a total of 120 of fencing and having 5 equal rectangular pens. Do you see how you can have different areas?

Now start defining some "variables" connected with your designs, and try to express two things in terms of them: (1) the total area enclosed; and (2) the total length of fencing used. Equating (2) to 120 m will give a relationship between your variables, and that will help you with the task of maximizing (1).