The correct answer is Nilgiris.
The Nilgiris district is a district in the Indian state of Tamil Nadu. It is located in the Western Ghats mountain range and is bordered by the states of Kerala, Karnataka, and Andhra Pradesh. The district is known for its tea plantations, forests, and wildlife sanctuaries. The Nilgiris district is also home to the Nilgiris National Park, which is a UNESCO World Heritage Site.
The other options are incorrect because they do not share their borders with three states. Krishnagiri district is located in the southern part of Tamil Nadu and is bordered by the states of Karnataka and Andhra Pradesh. Dharmapuri district is located in the northern part of Tamil Nadu and is bordered by the states of Karnataka and Andhra Pradesh. Tiruppur district is located in the western part of Tamil Nadu and is bordered by the states of Kerala and Karnataka.