AMC 12 2015a 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 \textbf{(B)}\ 4 \textbf{(C)}\ 5 \textbf{(D)}\ 6 \textbf{(E)}\ 8