A farmer has a 200 m fencingmaterial to enclose two adjacent sides of a rectangular...

nasriibraahim507

nasriibraahim507

Answered

2022-04-07

A farmer has a 200 m fencingmaterial to enclose two adjacent sides of a rectangular field. What dimensions should be used so that the enclose area will be a maximum?

Answer & Explanation

nick1337

nick1337

Expert

2022-04-19Added 573 answers

Let area be A and the sides of rectangular field be x and y;
So,

A=xy

Now, one side of the rectangle is already made with a fence.
There are 4 sides, two sides of x meters and two sides of y meters. Let a side of y meters be already fenced.

Then, the remaining three sides are to be fenced with a fence of 200 m length,

So,

2x+y=200

y=2002x
So,

A=x(2002x)

A=200x2x2

For area to be maximum,

dAdx=0 and d2Adx2<0

Now,

dAdx=200-4x

200-4x=0

x=50

Now,

d2Adx2=-4

Which is negative

Thus, x=50 is a maximum.

Now,

2x+y=200

2(50)+y=200

y=100

Thus, the required area is:

A=xy=50100=5000 m2

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get your answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?