2015 AMC 12A Problem 20

Isosceles triangles T and T' are not congruent but have the same area and the same perimeter. The sides of T have lengths of 5,5, and 8, while those of T' have lengths of a,a, and b. Which of the following numbers is closest to b?

\textbf{(A)}\ 3 \qquad\textbf{(B)}\ 4 \qquad\textbf{(C)}\ 5 \qquad\textbf{(D)}\ 6 \qquad\textbf{(E)}\ 8

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.