A farmer will build a rectangular pen for some goats. A wall will form one side of the pen. The farmer has 36 m of fencing to form the other three sides. The farmer plans to build the pen so that it has its maximum possible area. What will be the dimensions of the farmer’s goat pen? Enter your answers in the boxes. m by m

The dimensions are 9m by 18 m

Step-by-step explanation:

The perimeter will be

x+y+x for the three sides  ( the wall is the fourth side)

2x+y = 36

Solving for y

y = 36-2x

The area is x*y and we want it maxed

A =x( 36-2x)

   36x-2x^2

Taking the derivative

dA /dx = 36 - 2 * 2x

Setting this equal to zero to find the max

0 = 36 - 4x

4x = 36

Divide by 4

x = 36/4

x = 9

Now find y

y = 36-2x

y = 36 - 2*9

y = 36 - 18

  = 18

The dimensions are 9m by 18 m

the answer is b

step-by-step explanation: