Answer:
40.1 cm
Explanation:
You want the perimeter of the triangle with altitude 8.4 cm dividing the side into segments 12 cm and 4.1 cm.
Unknown sides
The lengths of the unknown sides can be found using the Pythagorean theoem.
c = √(a² +b²)
c = √(8.4² +12²) ≈ 14.65 . . . . . length of AC
and
c = √(4.1² +8.4²) ≈ 9.35 . . . . . length of CD
Then the sum of side lengths is ...
P = AC +CD +AD
P = 14.65 +9.35 +(12 +4.1) = 40.1 . . . . cm
The perimeter of triangle ACD is about 40.1 cm.