Answer:
Option A.
[tex]P=73.4\ units[/tex]
Step-by-step explanation:
see the attached figure with letters to better understand the problem
In this problem we have a triangle with a circle inscribed in it
so
[tex]A.F=A.B\\C.B=C.D\\E.F=E.D[/tex]
step 1
Find the length side B.C
[tex]C.B=A.C-A.B[/tex]
substitute the given values
[tex]C.B=23-14=9\ units[/tex]
step 2
Find the length side C.D
Remember that
[tex]C.D=C.B[/tex]
therefore
[tex]C.D=9\ units[/tex]
step 3
Find the length side E.D
we know that
[tex]E.D=E.C-C.D[/tex]
substitute the given values
[tex]E.D=22.7-9=13.7\ units[/tex]
step 4
Find the length side E.F
Remember that
[tex]E.F=E.D[/tex]
therefore
[tex]E.F=13.7\ units[/tex]
step 5
Find the length side A.F
Remember that
[tex]A.F=A.B[/tex]
therefore
[tex]A.F=14\ units[/tex]
step 6
Find the perimeter
[tex]P=23+22.7+13.7+14[/tex]
[tex]P=73.4\ units[/tex]
