A gardener wants to make a rectangular enclosure using a wall1 side and 120 m of fencing for the other 3 sides.find the values of x that gives the greatest area

Question

I need help please

Answer 1

P=2l+2w

120=2l+2w

60=l+w

A=lw

l=60-w

A=(60-w)w

A=60w-w²

take the first derivative to get 60-2w, 60-2w=0, 60=2w, and w=30

you want a square 30 m on a side

you don't need one side because of the wall

take that 30 m you don't need and add it to the opposite side to get 60 m

you have a rectangle 30 m by 60 m by 30 m by "the wall"

notice that a 30 by 60 rectangle is made up of two 30 by 30 squares put together side by side

the maximum area will always be a square so all you had to do was divide 120 by 4 to get 30 and take it from there

but you wrote applied derivative so you do it that way