Question

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

Answer 1

Answer:  5, 12, 13

Step-by-step explanation:

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

• Pythagoras theorem says that that the square of the longest side is equal to the sum of the squares of the other two sides.

5, 6, 11

Here, $11^2=121\\5^2+6^2=25+36=61\\\\But\ 121\neq61$

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

5, 9, 10

Here, $10^2=100\\5^2+9^2=25+81=106\\\\But\ 100\neq106$

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

5, 13, 18

Here, $18^2=324\\5^2+13^2=25+169=194\\\\But\ 324\neq194$

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

5, 12, 13

Here, $13^2=169\\5^2+12^2=25+144=169\\\\And\ 169=169$

Therefore, these line segments could create a right triangle.

Answer 2

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

• For the first option - 5, 6, 11

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

• For the second option - 5, 9, 10

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

• For the third option - 5, 13, 18

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

• For the fourth option - 5, 12, 13

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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