Why would the wall require more than a 30-40’ wide strip of land? No need to buy entire properties all along the border wall.
You're going to need to buy all the land on the Mexican side of the wall.
“Why would the wall require more than a 30-40’ wide strip of land?”
Ideally, the Border Patrol would like to maintain a 150 foot clear area to detect people near the barrier, including their patrol road. In urban areas, the 150 foot enforcement zone would be an exclusion area with a big barrier on each side, stadium lighting, constant camera surveillance, and wired with alarms - to achieve near 100% detection of intruders.
In rural areas, just a single barrier with a patrol road and some clear shoulders will suffice.
To determine what they need in a given location, they calculate detection time, intercept time and time required for illegals to disappear, in those different terrains. In some urban areas, fence jumpers can get into a car, run into a mall, or disappear through backyards in just one minute; while in very rural areas they might require days on foot.
Good barriers deter a lot of people, but if wired with technology (surveillance and alarms) they also serve as the primary tripwire to call the cops for an arrest. The 150 foot clearance gives them enough room for some really effective detection technology.