((image included))
if x = 27 inches, what is the perimeter of the figure above?
a. (108 + 54 + 54) inches
b. (54 + 108) inches
c. (364.5 + 729) inches
d. (27 + 54 + 81) inches

=204.13 inches.

Step-by-step explanation:

Using the side x, we can use sine to find the hypotenuse of the triangle with the angle marked 30°.

Sin 30 =x/hypotenuse.

sin 30 = 27/hyp

hyp= 27/sin 30

=54 inches

We can also find the adjacent as follows.

Cos 30 = adjacent/ 54

Adjacent= 54 cos 30

=46.77 inches

Using the angles marked 45 we can find the hypotenuse of the isosceles triangle.

sin 45= x/hypotenuse

sin 45 =27/hypotenuse

hypotenuse = 27/sin 45

=38.18 inches

The hypotenuse of both the triangles making the isosceles triangle are 38.18 inches long.

Perimeter = 54+ 46.77+27+ 38.18+38.18

=204.13 inches.

204.12 inches

Step-by-step explanation:

We can find the lengths of the unknown sides by applying these identities:

Observe the image attached. To find "a" we need to substitute the following values into :

And solve for "a":

To find "b" we need to substitute the following values into :

And solve for "b":

 To find "c" we need to substitute the following values into :

And solve for "c":

Since the triangle on the left is Isosceles, then:

Therefore, the perimeter is:

b

step-by-step explanation: