Answer:
feet and
feet
The least amount of fencing required = 40 feet.
Step-by-step explanation:
Let us take
be the length of the garden and
be width of the garden.
The area of the rectangular garden will be,
...{1}
Perimeter of the garden,
.
[ because one side of the garden is protected by a barn ]
Thus,

or
[using 1]

For points of maxima or minima

Since length cannot be negative,
is rejected.
Thus,


Hence at
, The perimeter
will be min.
On substituting
in
then 
Hence, the dimensions of the garden are:
feet and
feet
The perimeter,
feet i.e the least amount of fencing required.