2025 · Q54
Consider the following for the next two (02) items that follow: ABC is a triangle right-angled at B. The perimeter of the triangle is 24 cm, and the difference between the sum of the perpendicular sides and the hypotenuse is 4 cm. A circle is inscribed in the triangle. What is its radius?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A1 cm
- B1·5 cm
- C2 cm
- D2·5 cm
Explanation
Let the legs be a, c and the hypotenuse b: a + c + b = 24 and (a + c) - b = 4, giving a + c = 14 and b = 10. From a^2 + c^2 = 100 and (a+c)^2 = 196 we get 2ac = 96, so the area is ac/2 = 24. With semiperimeter s = 12, the inradius is r = Area/s = 24/12 = 2 cm. Hence option (c).