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.

Question

anonymous · Answer

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

anonymous · Answer

|dw:1363807138120:dw|
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)