Given that AD is the altitude of triangle ABC, then AD is perpendicular to BC, which means that angle ADC is a right angle, then
∠ADC = 90°
4x + 10 = 90
4x = 90 - 10
4x = 80
x = 80/4
x = 20
From the picture,
BC = BD + DC
Replacing with data,
BC = 2x + (3x - 4)
BC = (2x + 3x) - 4
BC = 5x - 4
Replacing with x = 20,
BC = 5(20) - 4
BC = 100 - 4
BC = 96
