A triangle has sides with lengths of 3, 7, and 2. What is the radius of the triangles inscribed circle?

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Answer 1 · 2016-02-06T01:21:08

This is not a triangle.

Use the triangle inequality theorem to see that these side lengths cannot form a valid triangle.

The theorem states that for any triangle with sides $a, b, c$ $a,b,c$ , the following three inequalities hold:

$a + b > c$ $a+b>c$

$b + c > a$ $b+c>a$

$c + a > b$ $c+a>b$

Here, we see that $3 + 2 > 7$ $3+2>7$ is untrue, so the sides do not describe a triangle.