Find The Height !

I came across a similar question a couple of yours ago in a math competition and came up with a formula ab/a+b it works here as well :D ............. 12x8/12+8 = 96/20 = 4.8

A(0,0), B(d,0) AB: y = 8d/x
C(0,12), D(d,8) CD: y-12 = -12d/x
AB/CD y/(y-12) = -8/12
y = 4.8

$\dfrac{1}{?}=\dfrac{1}{12}+\dfrac{1}{8}$ $\color{#BA33D6}(\text{note: This is a derived equation.})$

Then

$\dfrac{1}{?}=\dfrac{5}{24}$

Hence,

$?=\dfrac{24}{5}=$ $\boxed{4.8}$