SOLUTION: A circle is inscribed in a triangle with sides of lengths 3 cm, 4 cm, and 5 cm. The radius of this circle, in cm, is:
(A) 5/7 (B) 1 (C) 7/5 (D) 2 (E) none of these
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-> SOLUTION: A circle is inscribed in a triangle with sides of lengths 3 cm, 4 cm, and 5 cm. The radius of this circle, in cm, is:
(A) 5/7 (B) 1 (C) 7/5 (D) 2 (E) none of these
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Question 280082: A circle is inscribed in a triangle with sides of lengths 3 cm, 4 cm, and 5 cm. The radius of this circle, in cm, is:
(A) 5/7 (B) 1 (C) 7/5 (D) 2 (E) none of these Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! r = sqrt [(s - a)(s - b)(s - c)/s] where s = (a + b + c)/2
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s = (3+4+5)/2 = 6
r = sqrt(3*2*1/6)
r = 1 cm
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This is very similar to Heron's Law for the area of a triangle, the difference being that "s" inside the radical is a divisor rather than a multiplier.
It works for all triangles, not just right triangles.
