Let's call the sides in order a,b,c
A right triangle satisfies [tex]a^2+b^2=c^2[/tex]
An obtuse triangle has a longer long side, so that's [tex]a^2+b^2 < c^2[/tex]
An actute triangle is [tex]a^2+b^2>c^2[/tex]
We sort, square, add, and compare
4.
11,60,61
[tex]11^2 + 60^2 = 121+3600 = 3721[/tex]
[tex]61^2 = 3721 \quad\checkmark[/tex]
Answer: Right Triangle
5.
4,5,7
[tex]4^2+5^2= 16 +25=41[/tex]
[tex]7^2=49[/tex]
That's a bigger c, so
Answer: obtuse triangle
6.
7,19,25
[tex]7^2+19^2=49+361=410[/tex]
[tex]25^2 = 625[/tex]
Answer: obtuse triangle
