Question 1004129
Call the legs a and b.
The area is 
A = (1/2)ab
The perimeter is
P = a + b + sqrt(a^2 + b^2)
so that we need to solve
a + b + sqrt(a^2 + b^2) = (1/2)ab
sqrt(a^2 + b^2) = (1/2)ab - a - b
This might be very tricky to solve...
I tried some values and found 5, 12, and 13 work.