Single correct option
The two shorter sides of a right-angled triangle are 20 cm and 21 cm. What is the radius of the circle inscribed in the triangle?
- A. 6 cm
- B. 7 cm
- C. 14.5 cm
- D. 5.5 cm
Show answer and solution
Answer: (A) 6 cm
Hypotenuse = √(20² + 21²) = √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 ✓.
14.5 cm is the circumradius (half the hypotenuse) — a common distractor.
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 ✓.
14.5 cm is the circumradius (half the hypotenuse) — a common distractor.
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