the length and width of the sheep pen ,which is adjusted so that the enclosed area is maximum?

Question

a farmer wishes to build a rectangular sheep pen with 160m fence, using 1 side of an existing shed as the side.The shed is also rectangular of measurement 20m times20m. iif two sheep pen of the same size are build adjacent to each other,find^

Answer 1

let the width be x and the length will be
(160-x-(x-20))/2
area=[160-2x+20](x)/2
=90x-x^2
differentiating
90-2x=0
2x=90 and x=45
so the length =45 m
and -20+2breadth=160-90=70
2 breadth=90
breadth=45m

Answer 2

If you write the question out correctly, it would help.
I'll assume that the shed encloses only one side then you have:
160m+20m=180m
2*20m + 2*x = 180m
40m + 2x = 180m
2x = 140m
x = 70m
So you'd have a pen 20m by 70m which would use 160m of fencing material. 20m shed + 160m of fencing (20m+70m+70m)
|-------------------------|
| | 20 |
|-------------------------|
70