The length of side BC is 28 units.
Given:
Angle B = angle C (congruent angles)
AC = 2x + 7
BC = 4x
AB = 4x - 7
Objective:
Determine the length of side BC (4x)
Solution:
Since angle B is congruent to angle C, triangle ABC is an isosceles triangle. This means that the two sides opposite the congruent angles are also congruent. In this case, AC is congruent to AB.
Equating the expressions given for AC and AB:
2x + 7 = 4x - 7
Solving for x:
-2x = -14
x = 7
Now that we know x = 7, we can substitute it back into the expression for side BC:
BC = 4x = 4(7) = 28
Therefore, the length of side BC is 28 units.