notice the link above.... that's the relation of the sides in a triangle.
so, we start off by looking at the two smaller sides, nevermind the longest for a second.
on the second one listed there, 12, 5, 17, if we look at 12 and 5 only, how long can the last side be? well, can it be 17? well, 12+5 is 17, but only if 12 and 5 lie down flatly, only then we can put a 3rd side of 17 units long BUT, we're just going to end up with a flat-line, and lose the triangle, so, we can't have a longest leg of 17, because if we do, we don't have a triangle, just a flat-line, so no dice on that.
now checking the third one, 21, 7, 6, looking at 7 and 6, could be have a longest side of 21? wait a second!! 7+6 = 13, how in the dickens can we put a third side of 21 when 7 and 6 lying down flatly only give 13? so no dice there too.
anyhow the four one listed there is 9, 22, 11, again, looking at the small sides of 9 and 11, 9+11 = 20, how can we place a third side joining them that is 22 units long? no dice there either.
now looking at the first one listed, 10, 15, 24, we'll you already know.