Carina is drawing the plan of a rectangular garden that will have one of its sides along a straight stone wall. She bought $140 \mathrm{~m}$ of fencing, in pieces of $1 \mathrm{~m}$ each, to fence the other three sides. She cannot cut these pieces and must use all of them.

![](https://cdn.mathpix.com/cropped/2024_05_01_30c9a294a58a6e4b8190g-026.jpg?height=277&width=308&top_left_y=1872&top_left_x=1502)

(a) If the two sides adjacent to the stone wall are $40 \mathrm{~m}$ each, what will be the length of the third side?

(b) Is it possible for the longest of the sides to be fenced to be 85 m? And 65 m? Justify.
The sum of the lengths of the three sides (those that are not made of stone) is $140 \mathrm{~m}$.

(a) If the two sides adjacent to the stone wall are $40 \mathrm{~m}$ each, the two together are $80 \mathrm{~m}$, and the third side will be $140-80=60 \mathrm{~m}$.

(b) If the largest of the sides to be fenced is $85 \mathrm{~m}$, it cannot be adjacent to the stone wall, because in that case, these two sides would measure $85 \times 2=170 \mathrm{~m}$, which is greater than $140 \mathrm{~m}$. Therefore, it should be parallel to the stone wall, and in this case, each of the other sides would measure $27.5 \mathrm{~m}$, which is also not possible, since the fence is made of whole pieces of $1 \mathrm{~m}$ each.

The two sides that touch the stone wall can be $65 \mathrm{~m}$ each because in this case, the other would be $140-2 \times 65=10 \mathrm{~m}$, which does not contradict the given conditions.