Tower $A$ is $90 \ m$
Tower $B$ is $140 \ m$
$A$ and $B$ are $100 \ m$ apart
To find$: EF$ distance
By proportionality theorem for $\triangle \ AEF$ and $\triangle \ ACD $
$\dfrac{AE}{AC}=\dfrac{EF}{CD}$
$\implies\dfrac{20}{90}=\dfrac{EF}{100}$
$\implies EF=\dfrac{2}{9}\times 100=22.22 \ m$
So,the answer is $22.22 \ m$