By the Pythagorean's theorem, we know that in a right triangle the sum of the squares of the catheti must be equal to the square of the hypotenuse.
We will use that to see that the correct solution is {18, 24, 30}
Now let's see how to apply it.
We just need to see the different options and sum the squares of the two smaller values (which would be the catheti of the right triangle). If the sum is equal to the square larger value (the hypotenuse) then these segments could create a right triangle
1) {24, 30, 35}
we get:
24^2 + 30^2 = 35^2
1476 = 1225
These are not equal, so we can't use these segments to create a right triangle.
2) {12, 18, 30}
we get:
12^2 + 18^2 = 30^2
468 = 900
These are not equal, so we can't use these segments to create a right triangle.
3) {18, 24, 30}
we get:
18^2 + 24^2 = 30^2
900 = 900
These are equal, thus we can use these segments to create a right triangle.
4) {18, 24, 35}
18^2 + 24^2 = 35^2
900 = 1225
These are not equal, so we can't use these segments to create a right triangle.
Then the only correct option is the third set: {18, 24, 30}
If you want to learn more, you can read:
https://brainly.com/question/23103213
