She decides to trust a woman who is known for being a sea witch and knows this.
She trades her voice and signs a risky contract that can possibly ruin her life since it indicated that Ariel belonged to her.
She's is willing to go mute for the rest of her life and put the entire kingdom in danger just to get close to a cute guy she hardly knows.
What's really stupid is, she could have had any merman she wanted in the ocean. I mean, being the youngest of Triton's daughters, she wasn't the Crown Princess or heir (that was probably Aquata, the sister with the brown hair and blue tail), so it wouldn't matter who she married so long as the King was all right with it.
But nope. Ariel had to go and fall in love with a man she couldn't have, and then she gave up everything that most people cherish to be with him.