Which set of line segments could create a right triangle? 5, 6, 11 5, 9, 10 5, 13, 18 5, 12, 13

The set of line segments that could create a right triangle is 5, 12, 13.

To determine the set of line segments that could create a right triangle, we will determine which of set is a consist of Pythagoras triples. This can be done by testing for the option that satisfies the Pythagorean's theorem.

The Pythagorean's theorem states that "in a right-angled triangle, the square of the longest side (hypotenuse) equals the sum of squares of the other two sides"

Let the longest side (hypotenuse) be c and the other two sides be a and b.

Then, we can write that

a² + b² = c²

We will check if 5² + 6² = 11²

5² + 6² = 25 + 36 = 61

and 11² = 121

Since 61 ≠ 121

∴ 5² + 6² ≠ 11²

Thus, the line segments cannot create a right triangle

We will check if 5² + 9² = 10²

5² + 9² = 25 + 81 = 106

and 10² = 100

Since 106 ≠ 100

∴ 5² + 9² ≠ 10²

Thus, the line segments cannot create a right triangle

We will check if 5² + 13² = 18²

5² + 13² = 25 + 169 = 194

and 18² = 324

Since 194 ≠ 324

∴ 5² + 13² ≠ 18²

Thus, the line segments cannot create a right triangle

We will check if 5² + 12² = 13²

5² + 12² = 25 + 144 = 169

and 13² = 169

Since 169 = 169

∴ 5² + 12² = 13²

Thus, the line segments can create a right triangle

Hence, the set of line segments that could create a right triangle is 5, 12, 13.

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 5, 12, 13

Step-by-step explanation:

We know that for any right triangle, it must follow Pythagoras theorem.

5, 6, 11

Here,

Therefore, these line segments could not create a right triangle.

5, 9, 10

Here,

Therefore, these line segments could not create a right triangle.

5, 13, 18

Here,

Therefore, these line segments could not create a right triangle.

5, 12, 13

Here,

Therefore, these line segments could create a right triangle.

add all the numbers and check the ones place.

the answer is 486. as the ones place is more than 4, the estimation will be the next 10 ie, 490