If the triangle ABC is congruent to triangle ADC, then the sides BC and DC are corresponding sides. So, we can formulate the following equation:
12x - 15 = 3x + 30
12x - 15 - 30 = 3x (Subtracting 30 from both sides of the equation)
-15-30 = 3x - 12x (Subtracting 12x from both sides of the equation)
-45 = -9x (Adding like terms)
-45/-9 = x (Dividing by -9 on both sides of the equation)
5 = x (Dividing)
So, x = 5
Replacing x=5 in the equation of side BC, we have:
BC = 12*(5) - 15
BC = 60 - 15 (Multiplying)
BC = 45 (Subtracting)
BC= 45.