Two vertical poles AL and BM of height 4m and 16m respectively...

$\dfrac{4}{x + y} = \dfrac{z}{y} \left\{∵ ∆ LAB ∆ PNB\right\}$
⇒ y = \dfrac{z\left(x + y\right)}{4} \ldots . \left( i\right)$<br />Also, \dfrac{16}{x + y} = \dfrac{z}{x}\left\{∵ ∆ MBA ∆ PNA\right\}$
$⇒ x = \dfrac{z\left(x + y\right)}{16} \ldots . \left(ii\right)$
Adding equations \left(i\right) & \left(ii\right)$, we get, </p><p>$x + y = \left(x + y\right)\left(\dfrac{z}{4} + \dfrac{z}{16}\right)$⇒ z =$\dfrac{16}{5}$$