Question

Use Pythagorean theorem to decide which of these measures would be correct for the lengths of the sides of a right triangle.*2 pointsA) 2, 3, 4B) 7, 11, 14C) 8, 10, 12D) 9, 12, 15

Answer 1

To know which measure would be correct for the lengths of the sides of a right triangle, the Pythagorean triple is used.

`a^2+b^2=c^2`
`\begin{gathered} 2^2+3^2=4+9=13 \\ 4^2=16 \\ Hence, \\ 2^2+3^2\\e4^2 \\ It\text{ can not be the length of a right triangle} \end{gathered}`

Also,

`\begin{gathered} 7^2+11^2=49+121=170 \\ 14^2=196 \\ Hence, \\ 7^2+11^2\\e14^2 \\ It\text{ can not be the length of a right triangle} \end{gathered}`
`\begin{gathered} 8^2+10^2=64+100=164 \\ 12^2=144 \\ Hence, \\ 8^2+10^2\\e12^2 \\ It\text{ can not be the length of a right triangle} \end{gathered}`

Lastly,

`\begin{gathered} 9^2+12^2=81+144=225 \\ 15^2=225 \\ Hence, \\ 9^2+12^2=15^2 \\ It\text{ can be the length of a right triangle because it follows the Pythagorean theorem} \end{gathered}`

Therefore, OPTION D is correct.