Let your two lengths be x and y respectively.
Now, for a perimeter, we simply need to add the lengths together.
So, we can say P = 2(x + y), but P is given to be 38 ft.
So, we can say 2(x + y) = 38 and x + y = 19 (equation 1)
For the area, we do exactly the same. Area is worked out by multiplying the two different lengths.
Hence, we can write it as: xy = 48 (equation 2)
In short, your two equations are:
x + y = 19 (equation 1)
xy = 48 (equation 2)
You should be able to work out the rest from there.