Answer:
the first option is the answer, r = √6
Step-by-step explanation:
[tex]hypotenuse = \sqrt{opposite {}^{2} + adjacent {}^{2} } [/tex]
hypotenuse = q = √12
adjacent = p = √6
opposite = r
substitute the values into the hypotenuse formula
[tex]q = \sqrt{r {}^{2} + p {}^{2} } [/tex]
[tex] \sqrt{12} = \sqrt{r {}^{2} + ( \sqrt{6} ) {}^{2} } [/tex]
[tex]( \sqrt{12} ) {}^{2} = r {}^{2} +6[/tex]
[tex]12 = r {}^{2} + 6[/tex]
[tex]12 - 6 = r {}^{2} [/tex]
[tex]6 = r {}^{2} [/tex]
[tex] \sqrt{6} = r[/tex]
[tex]r = \sqrt{6} [/tex]
