Question : The radius of the incircle of a triangle whose sides are 9 cm, 12 cm, and 15 cm is:
Option 1: 9 cm
Option 2: 13 cm
Option 3: 3 cm
Option 4: 6 cm
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Correct Answer: 3 cm
Solution : To find: The radius of the incircle of a triangle whose sides are 9 cm, 12 cm and 15 cm. Since, $9^2+12^2=81+144=225=15^2$ So, this is a right-angled triangle. Let $p,b,$ and $h$ be Perpendicular, Base and Hypotenuse of the triangle, respectively. We know the radius of the incircle of a right-angled triangle, = $\frac{p+b-h}{2}$ = $\frac{9+12-15}{2}$ = $\frac{6}{2}$ = 3 cm Hence, the correct answer is 3 cm.
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