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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.

May 23, 2021

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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.

May 23, 2021