We know that
AD=8x-2
DH =7x-12
AH=18x-35
We need to find AD.
The solution of the question is based on the assumption that the point A, D and H are col-linear, i.e. they lie on the same line
⇒ AD + DH = AH
Substituting the values of AD, DH and AH in terms of x in the above equation, and solving the linear equation.
⇒ 8x-2 + 7x-12 = 18x-35
⇒ 15x-14 = 18x-35
⇒ -3x = -21
⇒ x = 7
Substituting the value of x in 8x-2 to determine the length of AD
AD = 8x-2
⇒ AD = (8×7)-2
⇒ AD = 56-2
⇒ AD = 54
Hence, AD is 54 units