Answer
$L$ = $5$
Work Step by Step
from the figure and given information, we have
$x^{2}+y^{2}$ = $L^{2}$
$\frac{dy}{dt}$ = $-0.15$ $m/s$
$\frac{dx}{dt}$ = $0.2$ $m/s$
$x$ = $3$ $m$
differentiating implicitly with respect to $t$ we get
$x^{2}+y^{2}$ = $L^{2}$
$2x\frac{dx}{dt}+2y\frac{dy}{dt}$ = $0$
$y\frac{dy}{dt}$ = $-x\frac{dx}{dt}$
$y(-0.15)$ = $-3(0.2)$
$y$ = $4$ $m$
thus
$3^{2}+4^{2}$ = $L^{2}$
$L$ = $5$
