Final answer:
To list the sides of triangle ABC in order from shortest to longest, we need to analyze the angles of the triangle and determine their relationships. By setting up an equation and solving for x, we can find the measures of the angles. The longest side will be opposite the largest angle.
Step-by-step explanation:
To list the sides of triangle ABC in order from shortest to longest, we need to analyze the angles of the triangle and determine their relationships. Given that angle A is 4x, angle B is 3x + 1, and angle C is 7x + 11, we can set up an equation:
4x + 3x + 1 + 7x + 11 = 180 (sum of angles in a triangle is 180 degrees)
Solving for x, we get x = 12.
Now, substituting x = 12 into the expressions for the angles, we find that angle A is 4 * 12 = 48 degrees, angle B is 3 * 12 + 1 = 37 degrees, and angle C is 7 * 12 + 11 = 95 degrees.
Since the sum of the angles of a triangle is always 180 degrees, we can conclude that the longest side of triangle ABC will be opposite the largest angle. So, side AC will be the longest side. The order from shortest to longest sides will be: AB, BC, AC.