The amount of fencing required is $L = a+2b$ and the area is constrained to be $A=ab=10000$. The analytical answer is easily obtained by calculus to be $a = \sqrt{2A}, b = \sqrt{A/2}$. Using numerical minimization gives the same result:
In [x]: A = 10000
In [x]: minimize(lambda X: X[0] + 2*X[1], (100,100), method='slsqp',
constraints={'type': 'eq', 'fun': lambda X: A-X[0]*X[1]})
Out[x]:
nit: 11
success: True
fun: 89.442719100358687
x: array([ 44.72135359, 22.36068276])
message: 'Optimization terminated successfully.'
njev: 11
status: 0
nfev: 44
jac: array([ 1., 2., 0.])
In [x]: np.sqrt(2*A), np.sqrt(A/2)
Out[x]: (44.721359549995796, 22.360679774997898)