Back to the Smallville airport, Lex Luther decides that bigger is better and proposes that the triangular shape for the runways for the airport be 10 km, 20 km and 35 km long. Clark Kent looks over the plan and says that it is impossible to build an airport with this triangular configuration. Clark is right . Why ?

consider the 35km side.

Even if you lay the other two down flat, they don't cover the longest side.
You need
20-10 < 35 < 20+10
to form a triangle. You do not have that.