Question

Which set of numbers could represent the lengths of the sides of a right triangle?

6, 9, 11

9, 12, 16

10, 15, 20

7, 24, 25

Answer 1

In right triangle:
a^2 + b^2 = c^2
where c is hypotenuse (side opposite to right angle) and also the longest of three sides.

For every set take largest number and threat it as c, then other two numbers threat as a and b (order doesn't matter because of commutative property of addition) and just test equality

First example:
a = 9
b = 6
c = 11

6^2 + 9^2 = 11^2
36 + 81 = 121
117 = 121
Not true, so 6, 9, 11 can't represent right triangle, analogously second and third set.

Fourth:
a = 7
b = 24
c = 25

7^2 + 24^2 = 625
49 + 576 = 625
625= 625 True, number can represent right triangle sides!

Answer 2

Your answer should be 7, 24, 25. Hope this helps!