Single correct option
The sides of a triangle are 13 cm, 14 cm and 15 cm. What is the radius of its inscribed circle?
- A. 3.5 cm
- B. 4 cm
- C. 4.5 cm
- D. 5 cm
Show answer and solution
Answer: (B) 4 cm
Semi-perimeter s = (13 + 14 + 15)/2 = 21.
Area by Heron's formula = √(21 × 8 × 7 × 6) = √7056 = 84 cm².
Inradius r = Area / s = 84/21 = 4 cm.
Tip: The 13-14-15 triangle is two right triangles (5-12-13 and 9-12-15) joined along the height 12; area = ½ × 14 × 12 = 84.
Area by Heron's formula = √(21 × 8 × 7 × 6) = √7056 = 84 cm².
Inradius r = Area / s = 84/21 = 4 cm.
Tip: The 13-14-15 triangle is two right triangles (5-12-13 and 9-12-15) joined along the height 12; area = ½ × 14 × 12 = 84.
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