Question

Ms. Browns class wants to build a rectangular pen for their rabbits. They have 24 ft of fencing . How long should each side be to give the rabbit the most space

Answer 1

You should draw all of the possible pens and calculate their areas to see which is largest.

Example: one pen could be

Answer 2

This pen would have a P=24 and A=20...Not the largest possible!

Answer 3

thats not what the question is asking

Answer 4

The most space for the rabbit would mean which pen has the greatest area, or square footage.

Answer 5

ur suppose to write an equation based on the infor but im not sure how

Answer 6

Are you learning about systems of equations right now?

Answer 7

ya

Answer 8

I think this is a related rates problem. You can take the derivative of the Area function and set it equal to 0. This will give you the peak area.

Answer 9

i thought it could be something like ths 24=12+2x but im unsure

Answer 10

Solve 24=2l+2w for w...

w= (24-2l)/(2)

Then substitute this in for the area equation

A=l*w
A=l*(24-2l)/(2)

Graph and look for the l value associated with the max

Answer 11

Related Rates is the best strategy, (re: Snowfire) if you're in calculus and know how to derive functions.

Answer 12

i have no clue how to derive functions

Answer 13

im in precal

Answer 14

It is as Sam said, you solve for either W or L in terms of the other to make it a one variable problem when you plug it back in. Then you plug that into the area function and solve.

Answer 15

Well put, thank you Snowfire

Answer 16

what is the l value

Answer 17

24=2W+2L
2W=24-2L
W=12-L

Then you look at the area function:

A=L*W
Plugging in the new W value from above gives you:
A=L*(12-L)
A=-L^2+12L
Now this is where I would normally use derivatives to finish the problem, but since you aren't expected to know that, you would look at its graph and find the highest point.