Respuesta :
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, [tex]11^2=121\\5^2+6^2=25+36=61\\\\But\ 121\neq61[/tex]
Therefore, these line segments could not create a right triangle.
5, 9, 10
Here, [tex]10^2=100\\5^2+9^2=25+81=106\\\\But\ 100\neq106[/tex]
Therefore, these line segments could not create a right triangle.
5, 13, 18
Here, [tex]18^2=324\\5^2+13^2=25+169=194\\\\But\ 324\neq194[/tex]
Therefore, these line segments could not create a right triangle.
5, 12, 13
Here, [tex]13^2=169\\5^2+12^2=25+144=169\\\\And\ 169=169[/tex]
Therefore, these line segments could create a right triangle.
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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