Can a right triangle have odd-length legs and even-length hypotenuse? Is it possible to have an even integer hypotenuse and odd integer legs (perpendicular and base) in a right triangle? If yes, please give an example. If no then please prove that.

Hint:
Suppose you have $A^2+B^2=C^2$ where $A=2a+1, B=2b+1, C=2c$
Substitute, expand and then take out terms with factors of $4$ 
