Numerical answer
A triangle has sides 13 cm, 14 cm and 15 cm. What is the radius (in cm) of its inscribed circle?
Show answer and solution
Answer: 4
Semi-perimeter s = (13 + 14 + 15)/2 = 21.
Heron's formula: Area = √[21 × (21 − 13)(21 − 14)(21 − 15)] = √(21 × 8 × 7 × 6) = √7056 = 84.
Inradius r = Area/s = 84/21 = 4 cm.
Tip: The 13-14-15 triangle is made of a 5-12-13 and a 9-12-15 right triangle joined along the height 12. The area is (14 × 12)/2 = 84, with no Heron's formula needed.
Heron's formula: Area = √[21 × (21 − 13)(21 − 14)(21 − 15)] = √(21 × 8 × 7 × 6) = √7056 = 84.
Inradius r = Area/s = 84/21 = 4 cm.
Tip: The 13-14-15 triangle is made of a 5-12-13 and a 9-12-15 right triangle joined along the height 12. The area is (14 × 12)/2 = 84, with no Heron's formula needed.
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