QA – Placement Quizzes | Mensuration 2D | Question 14

The sides of a triangle are 6 cm, 11 cm and 15 cm. The radius of its in-circle is:
(A) 3*(2)^0.5
(B) (4/5)*(2)^0.5
(C) (5/4)*(2)^0.5
(D) 6*(2)^0.5


Answer: (C)

Explanation: Let a, b, c be the sides of the triangle. Then, we know
Semi-perimeter = 1/2 * (a + b + c) = 1/2 * (6 + 11 + 15) = 16 cm.
Area = [s*(s-a)*(s-b)*(s-c)]^0.5 = [16*10*5*1]^0.5 = 20(2)^0.5 cm^2.
Therefore, Radius of in-circle = Area/Semi-perimeter = 20(2)^0.5 / 16 = (5/4)*(2)^0.5 cm.

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