when were the first plans for this building drawn up?
1929
Empire State Building
The Empire State Inc. consortium was announced to the public in August 1929.

what is the length of the empire state building UNANSWERABLE
wiki:7743530
Empire State Building [SEP] Early plans
Concurrently, Lamb's partner Richmond Shreve created "bug diagrams" of the project requirements. The 1916 Zoning Act forced Lamb to design a structure that incorporated setbacks resulting in the lower floors being larger than the upper floors. Consequently, the tower was designed from the top down, giving it a "pencil"-like shape.