A triangle has sides with lengths of 5, 1, and 3. What is the radius of the triangles inscribed circle?

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Answer 1 · 2016-02-01T19:15:10

The given triangle is not possible to be formed.

In any triangle the sum of any two sides must be greater than the third side.

If $a,b and c$ are three sides then
$a+b>c$
$b+c>a$
$c+a>b$

Here $a=5, b=1$ and $c=3$

$implies a+b=5+1=6>c$ (Verified)
$implies c+a=3+5=8>b$ (Verified)
$implies b+c=1+3=4cancel>a$ (Not Verified)

Since, the property of triangle is not verified therefore, there exists no such triangle.