jmc

Since we're dealing with percentages, the actual dimensions do not matter. Let $l$ and $w$ represent the dimensions of the TV screen. The current area is $lw$. If we increase $l$ by $20\%$, we end up with $l\left(1+\frac{20}{100}\right)=l\left(\frac{10}{10}+\frac{2}{10}\right)=\frac{12}{10}l$. Increasing the width results in $\frac{12}{10}w$. The new area is $\frac{12}{10}l\times \frac{12}{10}w=\frac{144}{100}lw=lw\left(1+\frac{44}{100}\right)$. The area increases by $\boxed{44\%}$.