Problem 112

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Problem 112: (2015 AMC12A, 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 $b$? $\textbf{(A)}\ 3 \qquad$ $\textbf{(B)}\ 4 \qquad$ $\textbf{(C)}\ 5 \qquad$ $\textbf{(D)}\ 6 \qquad$ $\textbf{(E)}\ 8$

Solution

Exercise 112: Solution

Isosceles triangles $T$ and $T'$ are not congruent but have the same area and the same perimeter. The sides of $T$ have lengths $4,4,$ and $6$, while those of $T'$ have lengths $a,a,$ and $b$. What is the value of $b$?

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