If the sides of a triangle measure 21cm, 35cm and 28cm, what is the measure of its in radius?(in cm)
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 7 cm.
The sides of the triangle measure 21 cm, 35 cm, and 28 cm.
Semi perimeter of a triangle, S = (A + B + C)/2 (A, B, C is the length of three sides of the triangle)
Area of a triangle = √S(S - A)(S - B)(S - C)
The measure of the inradius of a triangle = Area of the triangle/Semiperimeter of the triangle
Semi perimeter of the triangular park = (21 + 35 + 28)/2 = 84/2 = 42 m
Area of the triangular park = √42(42 - 21)(42 - 35)(42 - 28) = √42(21)(7)(14) = √86436 = 294 cm2
The inradius of triangle = 294/42 = 7 cm