A farmer plans to use 120 feet of fencing to fence a large r

A farmer plans to use 120 feet of fencing to fence a large rectangular region adjacent to his barn(no fence will be needed on the barn side), with two dividers perpendicular to the barn. Express the area of the region as a function of its length.

Solution

The farmer will fence the three sides of the rectangular region. And let l feet be the length and w feet is the width.

Therefore we get

2l +w=160

w=160-2l

And area = length*width

A(l)= l(160-2l)

A(l)= 160l -2l²