For a triangle whose perimeter measures 36 units, the radius of the inscribed circle is 3.Find the area of the triangle.
A) 27
B) 54
C) 108
D) None of These

Question

For a triangle whose perimeter measures 36 units, the radius of the inscribed circle is 3.Find the area of the triangle.
A) 27 
B) 54 
C) 108 
D) None of These

Quizplus · Accepted Answer

Let the sides of the triangle be $a$, $b$, and $c$. The semiperimeter is $s=\frac{a+b+c}{2}=18$ units. The area of the triangle can be expressed as $A=rs$, where $r$ is the radius of the inscribed circle. Thus, $A=3(18)=54$ square units. Therefore, the answer is $\boxed{	extbf{(B) }54}$.

For a Triangle Whose Perimeter Measures 36 Units, the Radius