Answer: In my opinion Penelope believed what he said.
Explanation: when Odysseus returned Ithaca after several years away he learnt that there were many suitors who wanred to marry Penelope so he decided to infiltrate as a beggar in his own home. In my opinion Penelope believed what that beggar was saying because she rested him and asked him several questions about Odysseus (he said that he had met Odysseus at Troy) such as his clothes and his friends.