Question

A farmer wants to fence off a 22,500 square feet area in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. How can the farmer do this so as to minimize the cost of the fence?

Answer 1

if we draw a line to divide the rectangle in half wouldn't it be parallel to two sides and not just one of the sides of the rectangle?

Answer 2

X*y=22500
s = 2x + 2y + x

Y= 22500/x

Min(3x +45000/x)

Answer 3

min{3 x+45000/x} = 300 sqrt(6) at x = 50 sqrt(6)

Answer 4

i don't know about this question
i'm still confused about that one part

Answer 5

so what would the final answer be?

Answer 6

Continue on with ivanbaj data:
x*y=22,500 sq ft
s (fence length) will be 2x + 2y +x (the extra x is the divider portion)
Also y in terms of x is 22,500/x (from the area formula)
substitute for the y in the amount of fence formula. getting
s=2x + 2(22500/x) + x
s=3x + 45000/x now differentiate
ds/dx= 3-45000x^-2 Set to 0 to find minima
\[3-45000/x ^{2}=0\] multiply thru by x^2 getting
\[3x ^{2}-45000=0\]\[3x ^{2}=45000\]
\[x ^{2}=15000\]\[x=\sqrt{15000}=\sqrt{2500*6}=50\sqrt{6}\]
\[y=22500\div 50\sqrt{6}=75\sqrt{6}\]
The cost of the fencing will be 300 times sq rt of 6 times what ever the fence cost per foot.

Get out of the water and practice these problems with the intent to learn procedures not 'just get answers"

Answer 7

radar i'm still confused about the question?
how can draw a line parallel to one of the sides of the rectangle without drawing a line parallel to two sides of the rectangle

Answer 8

it doesn;t make sense to me lol

Answer 9

It would be parallel to two of the sides and perpendicular to two of the sides.

Answer 10

right but why does it say draw it parallel to one of the sides?

Answer 11

That is to assure that you won't divide the rectangle by a diagonal. Noticed it didn't say that it would not be parallel to the other side.

Answer 12

i guess you are right lol

Answer 13

Yes, sometimes the instructions are more complex than the problem lol

Answer 14

i think it would be fun to the diagonal problem lol

Answer 15

Also English can sometimes lead to part of the problem (by the way it is used)

Answer 16

yes

Answer 17

Anyway I hope that the curiousmathstudent understands it. Have a nice day myininaya, and I have noticed you providing lots of good help. bye

Answer 18

you too
you're awesome too!