a developer plans to build a house around a 100ft 10,000 sq ft lake. people want to buy 100ft. how many lots can developer build

Do I take it that this is a square lake 100 ft x 100 ft? (=10,000 sq ft). If so it is small for a 'lake'.

If so the developer can build four 100 ft properties with a whole lake frontage, one each side of the lake. However, the question does not specify a whole lake frontage, so the developer could also build by staggering the properties around the lake. In this way he could get two on each facing side and one each on the other sides (draw it!), which makes 6 lots.

Indeed a really sneaky developer could get in 8 lots, four with a whole lake frontage, and four in the corner spaces, but that is really sneaky!