Identifying Lengths of the Sides of a Right Triangle. Which are the side lengths of a right triangle? Check all that apply. 3, 14, and square root 2056,11, and square root 15819, 180, and 1813, 19, and square root 3802, 9, and square root 85

Answer:The side lengths of a right triangle among the given options are3, 14, and square root 2052, 9, and square root 85Solution: Let us assume that the three sides of a right triangle are a, b and c So as per Pythagoras theorem, we know, [tex]a^{2}+b^{2}=c^{2}[/tex]Here for 3, 14, and square root 205, [tex](\sqrt{205})^{2}=205[/tex][tex]3^{2}+14^{2}=9+196=205[/tex]So this satisfies the right triangle For 6,11, and square root 158 [tex](\sqrt{158})^{2}=158[/tex][tex]6^{2}+11^{2}=157[/tex]So this do not satisfy the right triangle For 19, 180, and 181 [tex](\sqrt{181})^{2}=181[/tex][tex]19^{2}+180^{2}=32400[/tex]So this do not satisfy the right triangle Again for 3, 19, and square root 380 [tex](\sqrt{380})^{2}=380[/tex][tex]3^{2}+19^{2}=9+361=370[/tex]So this do not satisfy the right triangle For 2, 9, and square root 85 [tex](\sqrt{85})^{2}=85[/tex][tex]2^{2}+9^{2}=85[/tex]So, this satisfies the right triangle .