Single correct option
The legs of a right-angled triangle are 20 cm and 21 cm. What is the radius of its inscribed circle?
- A. 5 cm
- B. 6 cm
- C. 7 cm
- D. 8 cm
Show answer and solution
Answer: (B) 6 cm
Hypotenuse = √(20² + 21²) = √(400 + 441) = √841 = 29.
For a right triangle, inradius r = (a + b − c)/2 = (20 + 21 − 29)/2 = 6 cm.
Check with r = Area/s: Area = 210 and s = (20 + 21 + 29)/2 = 35, so r = 210/35 = 6. ✓
Tip: (20, 21, 29) is a Pythagorean triplet worth remembering.
For a right triangle, inradius r = (a + b − c)/2 = (20 + 21 − 29)/2 = 6 cm.
Check with r = Area/s: Area = 210 and s = (20 + 21 + 29)/2 = 35, so r = 210/35 = 6. ✓
Tip: (20, 21, 29) is a Pythagorean triplet worth remembering.
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