Math question but dont get one part of it?

For a long time, Tom's wife has complained that the farm animals get into her vegetable patch, trampling and eating the vegetables. Tom's solutions is to fence in the garden to keep the animals out. Looking in his shed, he discovers that he has a roll of fencing mesh that is 40 metres long.



Being a practical man, Tom wants to make the best use of the fencing mesh and provide his wife with the largest garden possible. He is only prepared to make a rectangular fence, and the side dimensions must be whole numbers.



Using the 16 metre wall as an entire or partial edge to the garden, and the 40 metres of fencing mesh, investigate the possible rectangular fences that can be constructed to produce a larger vegetable patch for Tom's wife. Draw a diagram of the final design showing the dimensions and how much of the shed's wall was used.

*** i do not understand what it means by "Using the 16 metre wall as an entire or partial edge to the garden" could someone please explain that bit.

Math question but dont get one part of it?
Only 3 sides of the rectangle require fencing because the wall will provide the fourth side.



Note that you can use all the wall, or less than all the wall, as the fourth side.
Reply:there exists a wall .... which provides a BOARDER rather than using fencing ....



if i use the wall (16') a side opposite that wall is also 16'

40 - 16 = 24' left of fence .....

24 / 2 sides is 12' sides

(12)(16) = 192 sq'





now only use 14' of the wall ...

40 - 14 = 26

26/2 = 13

(14)(13) = 182





now add 2' to wall

2' + 18' opposite = 20'

40 - 20 = 20

20 / 2 =10

(10)(18) = 180
Reply:Means that you have the wall that requires no fencing...so in your rectangle only 3 sides should be fenced
Reply:The 16 meter wall must be incorporated into one edge of the fenced area but that edge may be equal to or more than 16 meters (to qualify as complete or partial).
Reply:Imagine a prison cell which is rectangular. Three sides of the cell are made of metal grills while the 4th side is a wall. In your case the metal grills represent the 40m fencing mesh while the wall represents, well, the 16m long wall. The possible maximum dimension of the garden using all the 40m mesh is 16m x 12m. Two sides of the garden with fencing mesh are 12m while one side is 16m with mesh. The other side is the wall. So, 12+12+16 = 40. You used up all the fencing mesh.
Reply:You will use the wall as a fourth side thus allowing you to use the 40 metres of fencing for the remaining 3 sides. If you use the entire length of the wall, the garden will be 16 metres x 12 metres.