Why is the desired picture not displayed on TV via HDMI?

Question

HDMI

I have a Dell Vostro 5470 laptop, the screen resolution is 1366x768, when connected to a FullHD TV, Samsung offers to set the resolution to 1920x1080, I put it on, but the picture on the TV is stretched, although the FullHD TV, any other resolution, also does not fit, the picture is either large, or format 4: 3.
I used to have a laptop, I also connected it to the TV, but the resolution was set to 1600x900, and it just fit, there is no way to set it on Dell, but why is that? Is the TV FullHD? I bought an HDMI cable in a store, it seems to be of high quality, with ferrite rings and braided, but I took the cheapest one, maybe there is a problem in it?
PS graphics in the laptop hybrid Intel HD Graphics 4400+Nvidia GeForce GT740M
Stone Intel Core i5-4200U 1.6Ghz Haswell
4GB RAM
HDD WD 500GB