# Math

posted by .

A rectangular study area is to be enclosed by a fence and divided into two equal parts, with a fence running along the division parallel to one of the sides. if the total area is 384 ft^2, find the dimensions of the study area that will minimize the total length of the fence. How much fence will be required?

• Math -

p = perimeter = 3 L + 2 B

384 = L B so B = 384/L

p = 3 L + 768/L
dp/dL = 3 - 786 /L^2
= 0 for minimum
3 L^2 = 786
L^2 = 256
L = 16
B = 384/16 = 24
B/2 = 12
so two 12 by 16 areas

## Respond to this Question

 First Name School Subject Your Answer

## Similar Questions

1. ### shortest fence

this is my last question from applications of derivatives! A 216m^2 rectangular pea patch is to be enclosed by a fence and divided into two equal parts by another fence parallel to one of the sides. What dimensions for the outer rectangle …
2. ### math

i am having serious optimization problems. i don't get it!!! plz help. a 216-m^2 rectangular pea patch is to be enclosed by a fence and divided into two equal parts by another fence parallel to one of the sides. what dimensions for …
3. ### calculus

A 384 square meter plot of land is to be enclosed by a fence and divided into equal parts by a fence parallel to one pair of sides. What dimensions of the outer rectangle will minimize the amount of force used?
4. ### math

A rectangular field is to be enclosed by a fence. Two fences parallel to one side of the field divide the field into three rectangular fields. If 2400m of fence are available find the dimensions giving the max area.
5. ### Grade 11 Math

A rectangular dog run is to be enclosed by a fence and then divided into two smaller rectangular areas by a fence parallel to one of the sides. If 54m of fence is available, find the dimensions of the dog run of greatest possible area. …
6. ### Calculus 1

A rectangular field is enclosed by a fence and separated into two parts by a fence parallel to one of the sides. If 600 m of fencing is available, what should the dimensions be so that the area is a maximum?
7. ### Math

Jennifer plans to fence a rectangular area around her rectangular swimming pool. The total area enclosed by the fence, including the pool, should be 5 times the area of the pool alone. The pool is 20 feet by 17 feet. What is the total …
8. ### precalculus

A rectangular field is to be enclosed by a fence and divided into three equal rectangular parts by two other fences. find the maximum area that can be enclosed and separated in this way with 1200m of fencing.
9. ### calculus (optimization)

a rectangular study area is to be enclosed by a fence and divided into two equal parts, with the fence running along the division parallel to one of the sides. if the total area is 384 square feet, find the dimensions of the study …
10. ### area and perimeter

a farmer wishes to build a fence around a rectangular field and divide it into two equal parts as well.the dividing fence must be parallel to one of the side of the field. you are asked to find dimension of the field of maximum area …

More Similar Questions