Answer:
B. KI
Step-by-step explanation:
In a triangle, the shortest side is always opposite the smallest angle. Therefore, to determine which side of triangle IJK is the shortest side, we need to first work out the measures of its angles.
The interior angles of a triangle sum to 180°. Therefore:
[tex]m\angle I + m\angle J + m\angle K = 180^{\circ}[/tex]
Substitute the given angle expressions into this equation and solve for x:
[tex](5x + 1)^{\circ} + (3x + 5)^{\circ} + (11x + 3)^{\circ} = 180^{\circ}\\\\5x + 1 + 3x + 5 + 11x + 3 = 180\\\\19x + 9 = 180\\\\19x = 180 - 9\\\\19x = 171\\\\x = \dfrac{171}{19}\\\\x = 9[/tex]
Now, substitute the value of x into each angle expression:
[tex]m\angle I = (5(9) + 1)^{\circ} = 46^{\circ}\\\\m\angle J = (3(9) + 5)^{\circ} = 32^{\circ}\\\\m\angle K = (11(9) + 3)^{\circ} = 102^{\circ}[/tex]
As angle J is the smallest angle, the shortest side of the triangle is the side opposite this angle, which is:
[tex]\LARGE\boxed{\boxed{\textsf{Side $KI$}}}[/tex]
