We know that
AB = 10x + 4
BC = 4x - 3
AC = 12x + 16
We need to find x, AB and BC.
The solution of the question is based on the assumption that the point A, B and C are col-linear, i.e. they lie on the same line, and B lies between A and C
⇒ AB + BC = AC
Substituting the values of AB, BC and AC in terms of x in the above equation, and solving the linear equation.
⇒ 10x+4 + 4x-3 = 12x+16
⇒ 14x+1 = 12x+16
⇒ 2x = 15
⇒ x = 7.5
Substituting the value of x in 10x+4 to determine the length of AB
AB = 10x+4
⇒ AB = (10×7.5)+4
⇒ AB = 75+4
⇒ AB = 79
Hence, AB is 79 units
Substituting the value of x in 4x-3 to determine the length of BC
BC = 4x-3
⇒ BC = (4×7.5)-3
⇒ BC = 30-3
⇒ BC = 27
Hence, BC is 27 units