# Math

posted by Alex

A rectangular ﬁeld is to be fenced in on four sides with a fifth piece of fencing placed Parallel to one of the shorter sides, so that the ﬁeld is split in two parts. If 1600 m of fencing is available, ﬁnd the largest possible area for this enclosure. What dimensions give this maximum area?

1. Reiny

let the length be y m
and each of the shorter pieces (the width) be x
we know 2y + 3x = 1600
y = 800 - 3x/2

area = xy
= x(800-3x/2)
= 800x - 3x^2 /2

find the first derivative, set it equal to zero and find x
then find y, and the area xy

2. scott

xmax is on the axis of symmetry of the parabola

-b / 2a = -800 / (2 * -3/2) = 800 / 3

## Similar Questions

1. ### algebra

The length of a rectangular field is 18 m longer than the width. The field is enclosed with fencing and divided into two parts with a fence parallel to the shorter sides. If 216 m of fencing are required, what are the dimensions of …
2. ### math

the length of a rectangular field is 18 m longer than the width. the field is enclosed with fencing and divided into two parts with a fence parallel to the shoter sides. if 216 m of fencing are required to the shoter sides. if 216 …
3. ### Math

A rectangular field will be fenced on all four sides. Fencing for the north and south sides costs \$5 per foot and fencing for the other two sides costs \$9 per foot. What is the maximum area that can be enclosed for \$6000?
4. ### 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 …
5. ### Mathematics

A rectangular garden is to be fenced along four sides and is to be divided into three parts parallel to two of its shorter sides. Find the dimensions of the garden if the length is twice its width and the total fencing materials is …
6. ### math

The perimeter of a rectangular field is 300 meters. This field is to be fenced along three sides only. The fencing along its two lengths and one width is to be done at \$50 per meter. If the total cost of fencing is \$12,000, what are …
7. ### algebra

The perimeter of a rectangular field is 300 meters. This field is to be fenced along three sides only. The fencing along its two lengths and one width is to be done at \$50 per meter. If the total cost of fencing is \$12,000, what are …
8. ### math

A total of 800m of fencing material is used to enclose a rectangular field and to divide the field into four partitions by fences parallel to the width of the field. Find the dimensions of the largest are of the field that can be fenced.
9. ### Math1210

The perimeter of a rectangular field is 300 meters. This field is to be fenced along three sides only. The fencing along it's two lengths and one-width is to be done at \$50 per meter. If the total cost of fencing is \$12000, what are …
10. ### Calc.

A rectangular plot of land is to be fenced in using two kinds of fencing. Two opposite sides will use heavy-duty fencing selling for \$7 a foot, while the remaining two sides will use standard fencing selling for \$2 a foot. What are …

More Similar Questions