Posted by **steph** on Thursday, November 10, 2011 at 10:20pm.

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 -
**Steve**, Friday, November 11, 2011 at 10:58am
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

## Answer this Question

## Related Questions

- College Algebra - A farmer has 100 yeards of fencing with which to enclose two ...
- Math - A farmer wishes to put a fence around a rectangular field and then divide...
- Algebra - Math - A farmer has 100 yards of fencing with which to enclose two ...
- College Math - farmer wishes to fence a rectangular area along the river bank. ...
- calculus - Farmer Jones has 210 meters of fence. She wishes to construct a ...
- Math - a farmer wants to put a fence around a rectangular field and then divide ...
- Algebra 2 - A farmer wants to enclose 2 adjacent rectangular regions next to a ...
- Math - A farmer uses 1034 meters of fencing to enclose a rectangular region and ...
- Calc. - Please help solve this, A farmer has 600m of fence and wants to enclose ...
- cal - a rancher has 4000 feet of fencing for constructing a rectangular corral. ...