The smith family needs to fence in part of their backyard a

The smith family needs to fence in part of their backyard a rectangular pen for the family dog snoopy. The smiths decide to use existing fence along the back property line as one side of snoopy pen, and they purchase 100 feet of additional fencing to build the remaining three sides of the pen. What should the smith choose as the length and width of snoopy’s pen so that he will have the most space in which to play?

Solution

Let two sides be x and y

Then area A = x*y

From given data; x + 2y =100

From above two eqations,. A = ( 100 - 2y) *y

For maximum space /area , derivative of \" A w.r.t y \" should be zero

Therefore 100 - 4y =0

y = 25

From first equation , x = 50

Therefore length = 50

width = 25