+4 Georgie has a large rectangular garden area with
dimensions l metres by w metres which she wishes to
divide into three sections so she can grow different
vegetables. She plans to put a watering system along
the perimeter of each section. This will require a
total of 120 metres of hosing.
a. Show the total area of the three sections, A m2 is
given by A = 60w − 2w2 and hence calculate the
dimensions when the total area is a maximum.
+118608 It is necessary to make the assumption that the L length is cut into 3 so that the three gardens are all W wide.
The length of the 3 doesn't matter so long as the 3 add together to be L in length.
This is what it must be, the w sides are all parallel.
Now you can add up all the sides and put them equal to 120.
Then solve for L
and substitute A=WL to get the area given.
After that find dA/dW and put it equal to 0 to find the W that will make the Area maximum.
That should be enough to get you one your way.
Other answerers: Please allow Sumdud to do it from here.
If Sumdud needs more help he/she will show what they have done and ask for further assistance.
