Question

What is the largest area that can be enclosed with 400 feet of fencing? What are the dimensons of the rectangle?

Answer 1

what grade question is this?

Answer 2

Precal

Answer 3

is that all the info.

Perimeter=400

Answer 4

ahh

Answer 5

this question is easy :)

Answer 6

i think it's optimization if i am not wrong ?

Answer 7

2x+y = 400

Answer 8

x = short side ; y = long side of rectangle

Answer 9

What I thought it was 20=L+W

Answer 10

one long side of rectangle is not included because in question it says 3 dimensions

Answer 11

where do you get the 20 from ?

Answer 12

200 my bad

Answer 13

where did you get the 200 from ? lol

Answer 14

well if you take 400=2X+2y and divide it by two

Answer 15

right !!! ... L+W=200 would be if all four sides are using fence

Answer 16

oh ok. i read the question wrong. yes you can say 200 = l + w

Answer 17

so where do I go from there

Answer 18

first tell us are all 4 sides using fence ? or just 3 ?

Answer 19

4

Answer 20

ok then it's 200 = l + w

Answer 21

Okay I just dont know what to do after that how would I go about solving it

Answer 22

well you have to form another equation relating L and W

Answer 23

So like a function

Answer 24

well. if you recall the area function, it is LxW = Area

Answer 25

Yeah

Answer 26

so from your first perimeter equation, separate either L or W

Answer 27

lets say we separate L ; therefore L = 200 - W

Answer 28

okay

Answer 29

so now going back to the area equation, we see we have LxW = A ; but we know L = 200-W

Answer 30

okay

Answer 31

so A = (200-W)(W)

Answer 32

Okay

Answer 33

expand it out, A = 200W - W^2

Answer 34

thats what I got too

Answer 35

now set the area = 0 and take derivative

Answer 36

I dont know deriviates I am only in precal

Answer 37

oh ...

Answer 38

ok then

Answer 39

for max area the shape has to be square