Question 19. In ΔABC, m∠A = 4x, m∠B = 3x + 1, m∠C = 7x + 11. List the sides of ΔABC in order from shortest to longest.(1 point)
AC; BC; AB
BC; AB; AC
AC;AB; BC
To determine the order of the sides from shortest to longest, we need to find the values of x and evaluate the angles. Then, we can compare the angles to determine the sides.
m∠A = 4x
m∠B = 3x + 1
m∠C = 7x + 11
Since the sum of the angles in a triangle is always 180 degrees, we can set up an equation:
4x + 3x + 1 + 7x + 11 = 180
Combine like terms:
14x + 12 = 180
Subtract 12 from both sides:
14x = 168
Divide both sides by 14:
x = 12
Now, we can substitute this value back into the angle measurements:
m∠A = 4(12) = 48 degrees
m∠B = 3(12) + 1 = 37 degrees
m∠C = 7(12) + 11 = 95 degrees
Since angles A and B are smaller than angle C, we can conclude that side AC is the shortest, followed by side AB, and side BC is the longest.
Therefore, the correct answer is: AC; AB; BC.