SOLUTION: a farmer has $3000 to spend on fencing material to enclose a pasture.if the fencing material costs $15 per yard, what is the maximum area he can enclose in square feet?

Question 161660: a farmer has $3000 to spend on fencing material to enclose a pasture.if the fencing material costs $15 per yard, what is the maximum area he can enclose in square feet?
Found 2 solutions by checkley77, Alan3354:
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
3000/15=200 FT OF FENCING IS USED.
THE MAXIMUM AREA IS A CIRCLE.
THUS THE 200 FT OF FENCING WOULD BE THE CIRCUMFERANCE OF A CIRCLE:
200=2PIR
200=2*3.14R
200+6.28*R
R=200/6.28
31.847 FT. IS THE RADIUS OF THIS CIRCLE.
AREA OF THIS CIRCLE IS:
A=PIR^2
A=3.14*31.847^2
A=3.14*1,014.23
A=3,184.68 FT^2
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
a farmer has $3000 to spend on fencing material to enclose a pasture.if the fencing material costs $15 per yard, what is the maximum area he can enclose in square feet?
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He can buy 200 yards of fence (3000/15), which is 600 feet.
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The maximum area for a given perimeter is enclosed by a circle. In this case, the circle will have a circumference of 600 feet.
The radius is 600/2PI = 300/PI
The area = PI*r^2
Area = PI*(300/PI)^2
Area = 90000/PI = 28,648 sq feet.
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If it's a rectangular pasture, a square has the max area for 4-sided figures.
The square would be 150 by 150,
Area = 22,500 sq feet (less than the circle)

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