Which popular form of poetry that came out of Japan during this era uses three lines and totals seventeen syllables in the Japanese language?

a. haiku

b. limerick

c. tanka

d. sonnets

While you didn't provide any specific era during which any poetry should have came out. I can safely say that the answer you're seeking is A - Haiku.

I know the answer is haiku because the structure you describe; three lines and totals seventeen syllables in the Japanese language is exactly the main characteristic of haikus.