Question

Which set of side lengths is a Pythagorean triple?2, 3, 135, 7, 1210, 24, 2911, 60, 61

Answer 1

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.

Step-by-step explanation:

The Pythagoras theorem is given as:

`(hyp.)^2=(opp.)^2+(adj.)^2`

The hypotenuse side is the longest side.

Take the set 2,3,13

`\begin{gathered} (13)^2=(2)^2+(3)^2 \\ 169=4+9 \\ 169=13 \end{gathered}`

This is not true.

Take the sets 5, 7, 12

`\begin{gathered} (12)^2=(5)^2+(7)^2 \\ 144=25+49 \\ 144=74 \end{gathered}`

This is not true.

Take the sets 10, 24, 29

`\begin{gathered} (29)^2=(24)^2+(10)^2 \\ 841=576+100 \\ 841=676 \end{gathered}`

This is not true.

Take the sets 11, 60, 61

`\begin{gathered} (61)^2=(60)^2+(11)^2 \\ 3721=3600+121 \\ 3721=3721 \end{gathered}`

This is true.

So the set 11, 60, and 61 makes a Pythagorean triple.

Final Answer:

The last option is the correct answer.