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 $c$. Then the perimeter $P$ is given by $P=a+b+c=36$. Also, the area $K$ of the triangle is given by $K=rs$, where $r$ is the inradius and $s$ is the semiperimeter ($s=P/2$). Therefore, we have $K=3s=3(P/2)=54$. Thus, the answer is $\boxed{	extbf{(B) }54}$.

For a Triangle Whose Perimeter Measures 36 Units, the Radius