Question

A rectangular field is fenced and divided in half by another fence joining the midpoints of two opposite sides. Find the largest area of a field that can be fenced with 480 meters of fencing.

Answer 1

the answer is 120m x 80m i just need the work

Answer 2

total length of fence\[480=2l+3w\implies l=240-{3\over2}w\]
cost function is area:
\[A(l,w)=l\times w\\
A(w)=\left(24-{3\over2}w\right)w
\]
now, maximize A(w)