Answer
The depth of the lake is $403~m$
Work Step by Step
We can use $v = 1493~m/s$ as the speed of sound in freshwater at a temperature of $25^{\circ}C$. We can find the total distance the sound travels in the water:
$d = v~t = (1493~m/s)(0.540~s) = 806~m$
Since the sound reached the bottom of the lake and returned to the boat, the depth of the water is $\frac{806~m}{2} = 403~m$
