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

In a triangle, the sum of two sides will always be greater than the third. If 5, 9, and 10 are the line segments, 5+9=14 14>10, 10+9=19 19>5, and 5+10=15 15>9