According to the cosine theorem, A2 = B2+C2-2bcosa = (b+c) 2-2bcsa.

Therefore, if we substitute the above formula, we get S=2bc-2bccosA.

And S= 1/2bcsinA.

So we get 2bc-2bccosA= 1/2bcsinA, that is, 4-4cosA=sinA.

SinA=8/ 17 is obtained from the solution of sina2+COSA =1j.

So s =1/2bcsina = 4/17 * BC ≤ 4/17 * [(b+c)/2] 2 = 64/17.

So if and only if b=c=4 = true, the maximum value of s is 64/ 17.