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2015 AMC 12A Question 20

AMC12 · 2015 AMC 12A

Question 20

Isosceles triangles $T$ and $T'$ are not congruent but have the same area and the same perimeter. The sides of $T$ have lengths $5,$ $5,$ and $8,$ while those of $T'$ have lengths $a,$ $a,$ and $b.$ Which of the following numbers is closest to $b?$
  1. $3$
  2. $4$
  3. $5$
  4. $6$
  5. $8$