Okay, here we have this:
Considering the provided measures, we are going to determine if the triangle is a 45-45-90 triangle, a 30-60-90 triangle, or neither. So we obtain the following:
40, 50, 80:
We can see that a=40 and c=80=2a, so for it to be a 30, 60, 90 triangle, b must be 40 sqrt(3), however since it is not then this option is neither.
6√2, 6√2. 12:
Since two sides are equal, then we can think that it can be a 45, 45, 90 triangle, so let's confirm if the third side measures the same as the others multiplied by the root of 2:
[tex]\begin{gathered} 6\sqrt{2}\sqrt{2}=12 \\ 6\sqrt{2}^2=12 \\ 6\cdot2=12 \\ 12=12 \end{gathered}[/tex]
We observe that they are fulfilled perfectly, therefore in this case it is a 45, 45, 90 triangle.
31, 31√2. 62:
We can see that a=31 and c=62=2a, so for it to be a 30, 60, 90 triangle, b must be 31sqrt(3), however since it is not then this option is neither.
11, 11√3. 22:
We can see that a=11 and c=22=2a, so for it to be a 30, 60, 90 triangle, b must be 11sqrt(3), As we see that it is perfectly fulfilled, then it is a 30-60-90 triangle.
