Question

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)
AB; BC; AC
AC; BC; AB
BC; AB; AC
AC;AB; BC

Answer 1

Im sorry but thats wrong please check

Answer 2

To determine the order of the sides from shortest to longest, we can look at the angles and use the Triangle Inequality Theorem.

If we let x = 1, we can find the measures of the angles:
m∠A = 4(1) = 4
m∠B = 3(1) + 1 = 4
m∠C = 7(1) + 11 = 18

Since ∠A and ∠B have the same measure, we can conclude that side AB and side BC are congruent. The measure of side AC is unknown.

Based on the Triangle Inequality Theorem, with sides AB and BC being congruent, side AC must be longer than both of them.

Therefore, the order of the sides from shortest to longest is:

AB; BC; AC

Answer 3

I apologize for the mistake. Let's re-evaluate the problem.

Given:
∠A = 4x
∠B = 3x + 1
∠C = 7x + 11

To determine the order of the sides from shortest to longest, we need to compare the measures of the angles.

Since ∠A, ∠B, and ∠C are angles of a triangle, their measures must add up to 180 degrees.
4x + (3x + 1) + (7x + 11) = 180
14x + 12 = 180
14x = 168
x = 12

Now we can find the measures of the angles:
∠A = 4(12) = 48 degrees
∠B = 3(12) + 1 = 37 degrees
∠C = 7(12) + 11 = 95 degrees

To determine the order of the sides from shortest to longest, we can use the Law of Sines:
a/sinA = b/sinB = c/sinC

Let's denote the lengths of the sides as a, b, and c.
We have:
a/sinA = b/sinB = c/sinC

a/sin(48) = b/sin(37) = c/sin(95)

To find the order of the sides, we need to compare the ratios a/sin(48), b/sin(37), and c/sin(95).

Calculating the values:
a/sin(48) ≈ 1.08
b/sin(37) ≈ 1.07
c/sin(95) ≈ 1.11

Based on these calculations, the order of the sides from shortest to longest is:

AB; BC; AC