Do you have a test case that represents a valid scalene triangle?
(Note that test cases such as 1,2,3 and 2,5,10 do not
warrant a “yes” answer because there does not exist a triangle
having these dimensions.)

why cant dimensions of 1,2,3 exist? or 2,5,10?... is there some rule how 2 sides cant be equal to the third?

It's been a long time, but a scalene triangle is a triangle with no equal sides or angles. Maybe the given examples won't work because they create two equal angles?

why cant dimensions of 1,2,3 exist? or 2,5,10?... is there some rule how 2 sides cant be equal to the third?

Think of it this way: If you line the 1 and 2 sides in a line, they are a length of 3. This means that if you tried connecting their ends to the ends of the original long side of 3, they will lay perfectly on top of it, thus not being a triangle (just 2 overlapping lines). If the 2 and the 5 are connected, they make a length of 7, which isn't nearly long enough to connect to the ends of a line of 10. This is in contrast to a triangle that the two shorter sides equal a length longer than the original (example: 6,7,8). If you line up the 6 and 7, they have a length of 13, thus you will have to bend that line of 13 to make its ends connect to the ends of the line of 8, thus creating a triangle.

Serious, just get some graphing paper, try drawing a 6, 7, 13, triangle, once you've drawn the 6 on x-axis, 7 on the y axis, you'll quickly see that the remaining side cannot be 13 (it can be greater or less than 13, but if it's 13, then your triangle ends up being a straight line).

For a scalene triangle, try a 3,4,5 triangle. It's a right angled one with 5 as the hypotenuse.

Serious, just get some graphing paper, try drawing a 6, 7, 13, triangle, once you've drawn the 6 on x-axis, 7 on the y axis, you'll quickly see that the remaining side cannot be 13 (it can be greater or less than 13, but if it's 13, then your triangle ends up being a straight line).

For a scalene triangle, try a 3,4,5 triangle. It's a right angled one with 5 as the hypotenuse.

Do you even graph, bro?

Sure, you can't make any triangle with those dimensions, but you just described attempting to make a right triangle, but it is possible to make an acute triangle out of 3 lengths that are impossible to make a right triangle out of. Just because 3 lengths can't make a right triangle doesn't mean they can't be made into a triangle.

Sure, you can't make any triangle with those dimensions, but you just described attempting to make a right triangle, but it is possible to make an acute triangle out of 3 lengths that are impossible to make a right triangle out of. Just because 3 lengths can't make a right triangle doesn't mean they can't be made into a triangle.

im confused because on this website http://www.mathopenref.com/scalene.html im able to create almost any triangle including a 6,7,13 even tho someone said its illegal?

does anyone have a definitive answer on whats legal and not legal for triangles to exist?

im confused because on this website http://www.mathopenref.com/scalene.html im able to create almost any triangle including a 6,7,13 even tho someone said its illegal?

does anyone have a definitive answer on whats legal and not legal for triangles to exist?

They're not showing you decimal places, they are rounding up or down.
Any two sides added must be greater than the third side for the lengths to make a triangle.

Lol the two smaller sides of a triangle can't add up to be smaller than the longest sides.

Think of it like this: You have a straight line and another line parallel. If you bend that parallel line, you'd make a triangle with the other line, right? Well there's no way to do that unless that parallel line is longer than the other line. Otherwise, the corners wouldn't touch.

im confused because on this website http://www.mathopenref.com/scalene.html im able to create almost any triangle including a 6,7,13 even tho someone said its illegal?

does anyone have a definitive answer on whats legal and not legal for triangles to exist?

Are you trolling? How can you not understand this?

im confused because on this website http://www.mathopenref.com/scalene.html im able to create almost any triangle including a 6,7,13 even tho someone said its illegal?

does anyone have a definitive answer on whats legal and not legal for triangles to exist?