Question 106785
You do not have sufficient information given in the problem. There are many solutions that are possible. Also, you say the TV is square, but we know that TVs are not square. So, something is amiss.

Anyway, based on what you've said, we know from the Pythagorean formula that:
{{{d^2 = h^2 + w^2}}}, where d = diagonal, h=height, w = width.
If the TV were square, then the height and the width are the same, so,
{{{31^2 = h^2 + h^2 = w^2 + w^2}}}
{{{961 = 2h^2}}}
Dividing by 2
{{{961/2=x^2}}}
{{{480.5=x^2}}}
Taking the sqrt of both sides:
{{{21.920=x}}}