Question

Those are the answers, I put, I am confused on this question in general though, and would like help.

Answer 1

In order to find if the given sides are a triangle, the bigger side needs to be smaller than the sum of the other two sides:

`a\le b+c`

Looking at the options, the only one that is not a triangle is the first one (25 >= 11 + 13)

Then, to classify the triangles as acute, obtuse or right, we have:

`\begin{gathered} \text{right:} \\ a^2=b^2+c^2 \\ \text{acute:} \\ a^2b^2+c^2 \end{gathered}`

So, checking each option:

`\begin{gathered} 21,28,35\colon \\ 35^2=1225 \\ 21^2+28^2=1225 \\ 35^2=21^2+28^2\to right\text{ triangle} \\ \\ 9,15,19 \\ 19^2=361 \\ 9^2+15^2=306 \\ 19^2>9^2+15^2\to obtuse\text{ triangle} \\ \\ 8,12,14 \\ 14^2=196 \\ 8^2+12^2=208 \\ 14^2<8^2+12^2\to acute\text{ triangle} \end{gathered}`