Answer:
Option D. 9.2 units.
Step-by-step explanation:
In the ΔJKL ⇒ ∠J + ∠K + ∠L = 180
∠J + 67 + 74 = 180° ⇒ ∠J = 39°
In the given triangle JKL we apply law of sines
[tex]\frac{SinK}{JL}[/tex] = [tex]\frac{SinJ}{KL}[/tex] = [tex]\frac{SinL}{JK}[/tex]
Now we take [tex]\frac{SinK}{JL}[/tex] = [tex]\frac{SinJ}{2.3}[/tex]
[tex]\frac{Sin67}{JL}[/tex] = [tex]\frac{Sin39*}{2.3}[/tex]
JL = [tex]\frac{(2.3)Sin67}{Sin39}[/tex]
[tex]\frac{(2.3)(0.92)}{(0.6293)}[/tex] = 3.36 units
Now [tex]\frac{SinL}{JK}[/tex] = [tex]\frac{SinJ}{KL}[/tex]
[tex]\frac{Sin74}{JK}[/tex] = [tex]\frac{Sin39}{2.3}[/tex]
JK = [tex]\frac{2.3(Sin74)}{(Sin39)}[/tex]
= [tex]\frac{2.3(0.9613)}{(0.6293)}[/tex]
= 3.51 units
So perimeter of the triangle = 3.36 + 3.51 + 2.3 = 9.15 units ≈ 9.2 units.
Option D is the answer.
