pre-calc

posted by .

area of a rectangular region: a farmer wishes to create two rectangular regions bordering a river, by three fences perpendicular to the river and one connecting them. suppose that x represents the length of each of the three parallel pieces of fencing. she has 600 feet of fencing available.

a) what is the length of the remaining piece of fencing in terms of x?
b) determine a function A that represents the total area of the enclosed region.
c) give any restrictions on x
d) what dimensions of the total enclosed region would give an area of 22,500 feet squared?
e) what is the maximum area that can be enclosed?

  • pre-calc -

    600 feet total fence
    3 sides of x feet

    remaining side: 600 - 3x

    a(x) = x(600-3x) = 3x(200-x)

    naturally, 3x < 600, so x < 200 assuming an infinitesimally thin fence and poles of zero diameter. :-)

    22500 = 3x(200-x)
    -3x^2 + 600x - 22500 = 0
    x = 50 or 150

    max area achieved at x = 100
    a(100) = 30,000

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calc.

    Please help solve this, A farmer has 600m of fence and wants to enclose a rectangular field beside a river. Determine the dimensions of the fence field in which the maximum area is enclosed. (Fencing s required on only three sides: …
  2. College Math

    farmer wishes to fence a rectangular area along the river bank. No fence is required on the side adjacent to the river. The material for the fence costs P16.00 per meter for the side parallel to the river, P12.00 per meter for the …
  3. Algebra 2

    A farmer wants to enclose 2 adjacent rectangular regions next to a river. No fencing will be used next to the river. 60 meters of fencing will be used. What is the area of the largest region that can be enclosed. I need all of the …
  4. College Algebra

    A farmer has 100 yeards of fencing with which to enclose two adjacent rectangular pens both bordering a river. The farmer does not need to fence the side with the river. What should the dimensions of the two pens together (a rectangle) …
  5. Algebra - Math

    A farmer has 100 yards of fencing with which to enclose two adjacent rectangular pens - both bordering a river. The farmer does not need to fence the side with the river. What should the dimensions of the two pens Together (rectangle …
  6. Math

    a farmer wants to put a fence around a rectangular field and then divide the field into three rectangular plots by placing two fences parallel to one of the sides. if the farmer can only afford 1000 yards of fencing, what dimensions …
  7. Math

    A farmer uses 1034 meters of fencing to enclose a rectangular region and also to subdivide the region into three smaller rectangular regions by placing a fence parallel to one of the sides. Find the demensions that produce the greatest …
  8. cal

    a rancher has 4000 feet of fencing for constructing a rectangular corral. one side of the corral will be formed by a barn and requires no fence. three exterior fences and 2 interior fences partition the corral into 3 rectangular regions. …
  9. calculus

    Farmer Jones has 210 meters of fence. She wishes to construct a rectangular pen using the river as one side and dividing the pen into six separate rectangular pens as shown. What should the dimensions of the combined pens be to maximize …
  10. Math

    A farmer wishes to put a fence around a rectangular field and then divide the field into three rectangular plots by placing two fences parallel to one of the sides. If the farmer can afford only 1600 yards of fencing, what dimensions …

More Similar Questions