Answer :
Given:
The set of side lengths are:
2, 3, 13
5, 7, 12
10, 24, 29,
11, 60, 61
Required:
Find the set that is a Pythagorean triple.
Explanation:
The Pythagoras theorem is given as:
[tex](hyp.)^2=(opp.)^2+(adj.)^2[/tex]The hypotenuse side is the longest side.
Take the set 2,3,13
[tex]\begin{gathered} (13)^2=(2)^2+(3)^2 \\ 169=4+9 \\ 169=13 \end{gathered}[/tex]This is not true.
Take the sets 5, 7, 12
[tex]\begin{gathered} (12)^2=(5)^2+(7)^2 \\ 144=25+49 \\ 144=74 \end{gathered}[/tex]This is not true.
Take the sets 10, 24, 29
[tex]\begin{gathered} (29)^2=(24)^2+(10)^2 \\ 841=576+100 \\ 841=676 \end{gathered}[/tex]This is not true.
Take the sets 11, 60, 61
[tex]\begin{gathered} (61)^2=(60)^2+(11)^2 \\ 3721=3600+121 \\ 3721=3721 \end{gathered}[/tex]This is true.
So the set 11, 60, and 61 makes a Pythagorean triple.
Final Answer:
The last option is the correct answer.