help me!!!!

Question

a farmer has 120 feet of fencing to make a new rectangular yard for his chickens. if he only needs to use fencing on 3 sides as his barn if the 4th side, find the maximum area he could make his yard.

Answer 1

Here's another solution.

The maximum area is always a square.

120/4=30

You want a square 30 feet on each side, but one side is not needed because of the barn. Take this 30 feet and add it to the opposite side to get 60 feet.

You now have a rectangle 30 feet by 60 feet by 30 feet by a barn.

30*60=1800 square feet

Answer 2

If you call the 2 sides perpendicular to the barn x, you are left over with 120 - 2x fencing for the missing side. The area can then be represented as

 

A(x) = x(120 - 2x)   or

A(x) = -2x^2 + 120x

 

This one you can do without calculus. This is a parabola and it has it's max or min on the axis of symmetry. The formula for the axis of symmetry is x = -b/2a.

 

So our problem has x = -120/(-4) = 30 asa it's axis of symmetry. Plugging it in to the function we get

A(30) = -2(30^2) + 120(30) = -1800 + 3600 = 1800 sq ft.

 

If you wanted to find the dimensions of the pen, plug 30 into the original key to find x = 30 an 120-2(30) = 60.

 

Hope this helps.