Question

Jack has 800 feet of fencing to fence off a rectangular field that borders a straight river. HE DOESN'T NEED TO FENCE ALONG THE RIVER. What are the dimensions( L and W ) of the field that has the largest area? What is the largest area?

Answer 1

So, you are trying to fence an area next to a river. As you don't need to fence the rive, you can save one side of the rectangle and add more to the other tree sides
L
__________________
| |
W | | W
| |
~~~~~~~~~~~~~~~~~~~~~~~ river


We have 800 ft of fence to cover 2W + L so,
(1) 2W + L = 800

As a rectangle we can assume:
(2) L = 2W

As we saved the river side of fence the maximum area we can achieve is:
(3) A = (2W)(L)

Therefore you have 3 equations (1), (2) and (3) and three unknowns L, W, A. Can you solve?

Answer 2

omg awesome pic mathmind

Answer 3

I ended up getting all that, so does that mean that it comes out to roughly 266 feet for each? Great answer btw.

Answer 4

2W+L=800
and
we want to maxmize the area
area=WL
L=800-2W
so area=W(800-2W)=800W-2W^2
area'=800-4W
to find critcal numbers set area'=0
800-4W=0
4W=800
W=200
and
L-800-2(200)=400
so maximum area is 400(200)=80000

Answer 5

ops, i had a type on my (3) Area equation it's A = WL. And Myininaya got the solution!

thanks haha