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)
Responses
line AB;line BC;line AC
Image with alt text: line AB ; Image with alt text: line BC ; Image with alt text: line AC
line AC; line BC; line AB
Image with alt text: line AC ; Image with alt text: line BC ; Image with alt text: line AB
line BC;line AB; line AC
Image with alt text: line BC ; Image with alt text: line AB ; Image with alt text: line AC
line AC; line AB; line BC
line AC; line AB; line BC
To determine the order of the sides of triangle ABC from shortest to longest, we need to compare their lengths.
Given the angle measures:
∠A = 4x
∠B = 3x + 1
∠C = 7x + 11
To find the lengths of the sides, we need additional information such as side lengths or the relationship between the angles and sides (e.g., if the triangle is equilateral, isosceles, or scalene). Please provide more details to proceed further.
To determine the lengths of the sides of triangle ABC, we need to find the values of x and then substitute them into the given expressions for the angles. Once we have the angle measures, we can use the properties of triangles to compare the side lengths.
Let's start by setting up equations for the angles:
m∠A = 4x
m∠B = 3x + 1
m∠C = 7x + 11
Since the angles in a triangle add up to 180 degrees, we can write the 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 x = 12 into the expressions for the angles:
m∠A = 4(12) = 48 degrees
m∠B = 3(12) + 1 = 37 degrees
m∠C = 7(12) + 11 = 95 degrees
We can use the side-angle-side (SAS) congruence theorem to compare the lengths of the sides. In this case, we will compare angles A and B to determine which side is opposite the shortest angle. Since angle A is 48 degrees and angle B is 37 degrees, we can conclude that side AC is opposite the shortest angle.
Therefore, the sides of triangle ABC in order from shortest to longest are:
line AC; line AB; line BC
So, the correct answer is:
line AC; line AB; line BC