a) Yes, there is another way of solving it:
x * y = maximum area
2x + 2y = 100 meters. Rearrange equation to get: y = -x + 50
Substitute the second equation into the first to get:
x * (-x + 50) = maximum area
y = x * (-x + 50)
Now expand it and then differentiate it and set dy/dx = 0 to get the length of x.
This is also how you solve b. But instead of having 2x + 2y = 100, this time it is x + 2y = 100. Can you solve it now?