Most monitors are 72 pixels per square inch. 72 isn't a square number.

Are pixels wider than longer or wider than longer?

Why?

It's 72 pixels per inch, not 72 pixels per square inch so it doesn't matter that 72 isn't a square number.

I think that the pixels on a standard monitor are square and those on a tv set are rectangular, but you might want to check that.

A pixel is a pixel is a pixel, by any other name, it's still a pixel.
Here's a detailed definition:

Short for Picture Element, a pixel is a single point in a graphic image. Graphics monitors display pictures by dividing the display screen into thousands (or millions) of pixels, arranged in rows and columns. The pixels are so close together that they appear connected.

The number of bits used to represent each pixel determines how many colors or shades of gray can be displayed. For example, in 8-bit color mode, the color monitor uses 8 bits for each pixel, making it possible to display 2 to the 8th power (256) different colors or shades of gray.

On color monitors, each pixel is actually composed of three dots -- a red, a blue, and a green one. Ideally, the three dots should all converge at the same point, but all monitors have some convergence error that can make color pixels appear fuzzy.

The quality of a display system largely depends on its resolution, how many pixels it can display, and how many bits are used to represent each pixel. VGA systems display 640 by 480, or about 300,000 pixels. In contrast, SVGA systems display 800 by 600, or 480,000 pixels. True Color systems use 24 bits per pixel, allowing them to display more than 16 million different colors.

DianeD

A pixel in the abstract sense is as you describe, but I believe gringo is correct when he says that TV screens and some other devices have 'pixels' or rather phosphors on the screen that are not square. For an LCD monitor the pixels are as square as they come, but on some CRT screens a pixel is in fact a red, green and blue dot arranged in a triangle shape - they are just so close together that you see them as one dot.

I was so curious about this topic that I did a bit of research and came up with this explanation about the usage of pixels in TV's, monitors and very large screen TV's. You can read about it here at How Stuff Works.

Just had to know,
DianeD