Question

a farnmer decides to enclose a rectangular garden, using the side of a barn retriceone side of the rectangle. What is the maximum area that the farmer can enclose with 60ft of fence? What should the dimensions of the garden be to give this area?

Answer 1

do you know the length of the side of the barn?

Answer 2

no this is all the question gives

Answer 3

x+y=60 formula for total amount of frencing
xy=area formula for area

y=60-x
x(60-x) = 60x - x^2 =area
da/dx = 60-2x
set equal to 0 to find max
60-2x=0
2x=60
x=30

sub back in
30+y=60
y= 30
length x width
30 x 30

My guess.

Answer 4

jake, that is incorrect. the perimeter is 2(x+y), not x+y

Answer 5

OK, he's got 60 feet of fence and he's got one side already (the barn).

If we let the side length be x then the area is

A = x (60-2x) = 60x -2x^2 which we can differentiate to get

60-4x = 0 at max x and x = 15 feet.

So max Area is 15(60-30) = 450 sq ft. (I hope)

Answer 6

Oh yes, sorry, i forgot. haha.

EDITED*
x+y=30 formula for total amount of frencing
xy=area formula for area
y=30-x
x(30-x) = 30x - x^2 =area
da/dx = 30-2x
set equal to 0 to find max
30-2x=0
2x=30
x=15
sub back in
15+y=60
y= 45
length x width
15 x 45

Answer 7

I agree with estudier x:

Answer 8

2x+y=60 formula for total amount of frencing
xy=area formula for area
y=60-2x
x(60-2x) = 60x - 2x^2 =area
da/dx = 60-4x set equal to 0 to find max
60-4x=0
4x=60
x=15 sub back in
30+y=60
y= 30
length x width 30 x 15 =450