To find out if these numbers make a right triangle, you need to use the equation a²+b²=c².
For the first set of lengths, plug in the numbers in their appropriate locations in the equation. 8²+10²=12². Make sure you put the largest number as the c², as it is the hypotenuse. You then solve the equation by squaring each of the numbers, then adding the a² and b².
8²+10²=12²
64+100=144
164≠144
If the two values are not equal, then the triangle is not right. Use the same equation (a²+b²=c²) to find if the other sets of lengths get a right triangle. Make sure to always put the hypotenuse value as the c².