∠ADC is a right angle [definition of altitude]. ∠ADC = 4x - 10, and since all right angles are 90° >> 4x - 10=90 >> 4x -10+10= 90+10 >> 4x=100 >> 4x/4=100/4 >> x=25.
BD+DC=BC [Between-ness of points] >> 4x + 5x -3=BC >> we know that x=25, so by substitute property >> 4*25+5*25 -3=BC >> 100+125 -3=BC >> 222=BC
