Question

What is the perimeter of the figure

Answer 1

Answer:

Option A.

$P=73.4\ units$

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

$A.F=A.B\\C.B=C.D\\E.F=E.D$

step 1

Find the length side B.C

$C.B=A.C-A.B$

substitute the given values

$C.B=23-14=9\ units$

step 2

Find the length side C.D

Remember that

$C.D=C.B$

therefore

$C.D=9\ units$

step 3

Find the length side E.D

we know that

$E.D=E.C-C.D$

substitute the given values

$E.D=22.7-9=13.7\ units$

step 4

Find the length side E.F

Remember that

$E.F=E.D$

therefore

$E.F=13.7\ units$

step 5

Find the length side A.F

Remember that

$A.F=A.B$

therefore

$A.F=14\ units$

step 6

Find the perimeter

$P=23+22.7+13.7+14$

$P=73.4\ units$