In ABC, m<A = 4x, m<B = 3x + 1, m<C = 7x + 11. List the sides of ДАВС in order from shortest to longest. (1 point)
0 AC; BC; AB
• BC; AB; AC
• AB; BC; AC
• AC; AB; BC
To determine the order of the sides from shortest to longest, we need to compare the lengths of AC, BC, and AB.
Given:
m<A = 4x
m<B = 3x + 1
m<C = 7x + 11
Since ABC is a triangle, the sum of the angles must equal 180 degrees:
m<A + m<B + m<C = 180
Substituting the given angle measures:
4x + 3x + 1 + 7x + 11 = 180
14x + 12 = 180
14x = 168
x = 12
Now we can find the length of each side:
AC = 4x = 4(12) = 48
BC = 3x + 1 = 3(12) + 1 = 36 + 1 = 37
AB = 7x + 11 = 7(12) + 11 = 84 + 11 = 95
From shortest to longest, the sides are:
BC; AC; AB
Therefore, the correct answer is:
• BC; AC; AB