Question

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

Answer 1

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.