Single correct option
The two perpendicular sides of a right-angled triangle measure 20 cm and 21 cm. What is the radius of its inscribed circle?
- A. 5
- B. 7
- C. 6
- D. 14.5
Show answer and solution
Answer: (C) 6
Hypotenuse = √(20² + 21²) = √(400 + 441) = √841 = 29 cm.
For a right triangle, inradius r = (a + b − c)/2 = (20 + 21 − 29)/2 = 6 cm.
Check with r = Area/semi-perimeter: Area = ½ × 20 × 21 = 210; s = (20 + 21 + 29)/2 = 35; r = 210/35 = 6 ✓.
Why others fail: 14.5 is the circumradius (half the hypotenuse); 5 and 7 are slips.
Tip: Memorise r = (a + b − c)/2 for right triangles – it saves the area computation.
For a right triangle, inradius r = (a + b − c)/2 = (20 + 21 − 29)/2 = 6 cm.
Check with r = Area/semi-perimeter: Area = ½ × 20 × 21 = 210; s = (20 + 21 + 29)/2 = 35; r = 210/35 = 6 ✓.
Why others fail: 14.5 is the circumradius (half the hypotenuse); 5 and 7 are slips.
Tip: Memorise r = (a + b − c)/2 for right triangles – it saves the area computation.
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