Question

a man wishes to fence in a rectangular enclosure of area 128m^2.one side of the enclosure is formed by part of the brickwall already in place .what is the least possible length of fencing required for the other three sides?

Answer 1

answer to a square is 33.941125496954281171240529381033
but if one side is 16 then you only need 32 of fencing

Answer 2

A=xy=128
xy=128
y=128/x
assuming y is the length brickwall then the side parallel to has same length
P=y+2x
P=128/x+2x
P'=-128/(x^2)+2
set P'=0
-128/(x^2)=-2
128/(x^2)=2
128=2x^2
64=x^2
x=8
y=128/8=16

Answer 3

myininaya what happen to your solution? one side that you had as 128/sqrt(128) is what I got.
and I miss reading the problem?
that works if a square but i tried a random side of 16 and found 128/16 = 8 therefore only 32 feet needed

Answer 4

we dont want fencing on the brickwall

Answer 5

we want fencing on 3 sides not 4

Answer 6

I agree but is the question the total length of fence or keeping each side the shortest?

Answer 7

so the answer is P=y+2x=16+2(8)=16+16=32

Answer 8

it is the sum of the 3 side's lengths when we have found the shortest lengths possible

Answer 9

I agree with your answer but I missed something with the question. I got the answer just because I had seen enough of these problems and knew to factor 128 in to common numbers 2,64 4,32 8,16 and so on.

Answer 10

i assume you taken calculus

Answer 11

we want to minimize

Answer 12

so we need P'

Answer 13

thanx guys

Answer 14

and set =0

Answer 15

to find critical numbers

Answer 16

there is only one critical number
and it is a minimum

Answer 17

true but why use a sledgehammer to kill a fly? most are looking for answers not the correct method. that is why I checked your answer as the best because the solution was given.

Answer 18

lol

Answer 19

dont you think it is funner to kill a fly with a sledgehammer