Can the set of numbers 3, 4 and 7 be the side lengths of a right triangle

The side can not form a triangle because the sum of any two sides must be greater than the other side: 3 + 4 = 7 and this is not greater than 7

Also, in order for the sides to form a right triangle a² + b² = c² where c is the longest side
3² + 4² ? 7²
9 + 16  ? 49
25 ≠ 49
ANSWER: No, the numbers cannot be a right triangle side lengths

In order for a set of numbers to be lengths of a right triangle, they must be able to be plugged into the Pythagorean Theorem of a² + b² = c² where a and b are the smaller lengths and c is the biggest one. 

3² + 4² = 7²
9 + 16 = 49
25 ≠ 49

This is not a right triangle. In order for it to be one, your hypotenuse would have to be a 5.