Answer:
x = 84 ft the largest side of the pens
y = 56 ft the common side is that length
Step-by-step explanation:
Let call x the total length of one side, and y the other side, and the common side such as:
p(perimeter) = 336 = 2x + 3y y = ( 336 - 2x ) / 3
And the area of the whole area
A(t) = x * y A(x) = x* (336 - 2x)/3 A(x) = [336x - 2x² ]/3
Taking derivatives both sides of the equation
A´(x) =[ ( 336 - 4x )*3]/9 ⇒ A´(x) = 0 ( 336 - 4x )*3 = 0
336 - 4x = 0
x = 336/4
x = 84 ft and y = ( 336 - 2x ) / 3 y = ( 336 - 168)/3
y = 56 ft
