To determine if the lengths given create a right triangle you can set up equations. According to Pythagorean Theorem, the square of the longest side would equal the sum of the squares of the smallest 2 sides.
1st given set: 15 + 25 < 64 This CANNOT be a right triangle. The sum of the 2 smallest sides is less than the sum of the longest side.
2nd given set: 64 + 100 < 256 This CANNOT be a right triangle. Again, the sum of the 2 smallest sides is less than the sum of the longest side.
3rd given set: 3,4,5 This CAN be a right triangle. These 3 numbers are multiples of 7, and if you factored 7 out of them you are left with 3,4,5 which is a triple. Triples are combinations of numbers that are guaranteed to create right triangles. 3,4,5 is one of the most basic triples. Hope this helps!
