Question

A farmer wishes to fence off part of paddock but only has 120 meters of fencing material avaibale. the farmer decides to use part of an exitting fence along one side with the 120 metres of avaible material forming the other 3 sides of a rectangle. What are the dimension of the rectangle to give a maximum fenced off area?

Answer 1

if this means you have 120 feet for 3 sides, use half for side opposite free side and split the other half in two, so dimensions would be 60 by 30

Answer 2

\[x+2y=120\]
\[x=120-2y\]
\[A=xy\]
\[A(y)=y(120-2y)=120y-2y^2\] this is a parabola that opens down, max at vertex
\[-\frac{b}{2a}=-\frac{120}{-2\times -2}=30\] as promised

Answer 3

Thanks