"When these tenements were built, there were almost no laws regulating tenement construction. In the early 1860s, the laws mandated that there be a fire escape on a building, that it have a strong, fireproof party wall."
-The Architecture and Development of New York City

Measurements

Tenement buildings were 25 foot lots. Buildings had 4 apartments per floor and 3 rooms per apartment.  There was also only 1 window in each apartment.
"They were fine, almost generous, so long as the City was of medium size and its residents lived in row houses.  But soon enough a swift influx of population required not single-family houses but multiple dwellings.  Now, on the lot which had been designed for a single row houses, a building inhabited by 20 or more families rose five, even six, stories high." 
-Ruth Limmer and Andrew S. Dolkart