Answer:
Option D. 26 in
Step-by-step explanation:
In the given ΔABC
Side BC = 2 + 5 = 7 in.
Side AB = AD + BD = 6 + 2 = 8 in. [ since length of tangents BD and BF to the circle inscribed are equal ]
From Pythagoras theorem
AC² = AB² + BC² = 8² + 7² = 64 + 49 = 113
AC = √113 = 10.63 in
Now perimeter of ΔABC = AB + BC + AC = 8 + 7 + 10.63 = 25.63 ≈ 26 in
Therefore Option D. 26 in is the correct choice.
