Blender make hair length vary in size, but keep "origin point" to be face of object

So in blender I am making a rug/carpet without thickness, so it's only one face, and when I add hair particles (and change some settings) it looks fine, however each hair is of a certain length like so:

I tried changing the random setting under Children -> Roughness, and although that does solve the same-length problem, it brings on a new one, the hairs can start from below my face.