Let `c` represent the longest side of the triangle. `a,b` will represent the other two sides.

(1) side lengths 26,20,17

This is an acute triangle. Here `c^2<a^2+b^2`

(2) side lengths 26,20,14

This is an obtuse triangle. Here `c^2>a^2+b^2`

(3) side lengths 26,10,24

This is a right triangle. Here `c^2=a^2+b^2` (You might also recognize the sides as the multiple of a basic pythagorean triplet -- namely 5-12-13)

(4) side lengths 26,10,15

This is not a triangle. From the triangle inequality theorem we know that the sum of any two sides of a triangle must be longer than the third side. Here 10+15=25<26.