Question: What is the radius of a circle inscribed in a triangle with sides 7 cm, 8 cm, and 9 cm?

Options:

1. 4 cm
2. 3 cm
3. 5 cm
4. 6 cm

Correct Answer: 3 cm

Solution:

Semi-perimeter s = (7 + 8 + 9)/2 = 12 cm. Area = √[s(s-a)(s-b)(s-c)] = √[12(12-7)(12-8)(12-9)] = √[12*5*4*3] = 12√5 cm². Radius = Area/s = 12√5/12 = √5 cm.