The length of the diagonal of the TV screen is 42 inch and its aspect ratio is 16:10. The aspect ratio is the length of the the longer side divided by the length of the shorter side. If the length of the shorter side L, the length of the longer side is 1.6*L.

Now use Pythagoras' Theorem to get L^2 + (1.6*L)^2 = 42^2

=> L^2(1 + 2.56) = 42^2

=> L^2 = 495.5

=> L = 22.25

The longer side of the TV screen is 35.61

**The required dimensions of the TV screen are 22.25 inch and 35.81 inch.**