Let l be the length of the TV, in inches. Since the diagonal of the TV forms a right triangle with the length and width (legs), then we can use the Pythagorean Theorem to find l:

\(\displaystyle{l}^{{2}}+{14}^{{2}}={50}^{{2}}\)

\(\displaystyle{l}^{{2}}+{196}={2500}\)

\(\displaystyle{l}^{{2}}={2304}\)

\(\displaystyle{l}=\sqrt{{2304}}\)

\(l=48\)

So, the length of the TV is 48 inches.