SOLUTION: A rectangular area is to be enclosed and then divided into thirds by two fences across the parallel to one pair of the sides. If the area to be enclosed is 1,250 square feet, what

Algebra ->  Surface-area -> SOLUTION: A rectangular area is to be enclosed and then divided into thirds by two fences across the parallel to one pair of the sides. If the area to be enclosed is 1,250 square feet, what       Log On


   

Question 1156708: A rectangular area is to be enclosed and then divided into thirds by two fences across the parallel to one pair of the sides. If the area to be enclosed is 1,250 square feet, what dimensions will lead to the use of a minimum amount of fence.
Please show a graph for this math
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Let the width be x; then the length is 1250/x.

The total length of fencing is 4 times the width plus two times the length.

f%28x%29+=+4x%2B2500%2Fx

Find the minimum amount of fencing by taking the derivative and finding when it is zero.

df%2Fdx+=+4-2500%2Fx%5E2

4-2500%2Fx%5E2+=+0+
4+=+2500%2Fx%5E2
x%5E2+=+2500%2F4+=+625
x+=+25

The dimensions of the field that uses the minimum length of fencing are x and 1250/x:
width x = 25
length 1250/x = 1250/25 = 50

The minimum amount of fencing required is 4(25)+2(50) = 200.

graph%28400%2C400%2C-10%2C50%2C-50%2C450%2C4x%2B2500%2Fx%2C200%29