A circular sprinkler is placed inside a triangular garden with sides 13 m, 14 m, and 15 m. What is the radius of the sprinkler if it touches all three sides of the triangle?
Show answer & explanation
Correct answer: A
Explanation
Has been given :
Sides of triangle = 13 m, 14 m, 15 m
According to the formula:
Radius r = area / semiperimeter
Semiperimeter s = (13 + 14 + 15) / 2= 21
Area = √[s(s − a)(s − b)(s − c)]
= √[21(21 − 13)(21 − 14)(21 − 15)]
= √[21 × 8 × 7 × 6]
= √7056
= 84
r = area / perimeter = 84 / 21 = 4
Radius of sprinkler = 4 m