Final answer:
To match the given information with the answers, we can use the Pythagorean theorem. Only the answer 3√3 matches the given information.
Step-by-step explanation:
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. We can use this theorem to match the given information with the corresponding answers.
2√13: This answer matches the hypotenuse of a right triangle with legs of length 2 and √5. Substitute the values into the Pythagorean theorem: √(2^2 + (√5)^2) = √(4 + 5) = √9 = 3. Therefore, this answer does not match the given information.
√5: This answer matches the legs of the right triangle with a hypotenuse of length 2√13. Substitute the values into the Pythagorean theorem: √((√5)^2 + (√5)^2) = √(5 + 5) = √10. Therefore, this answer does not match the given information.
3√3: This answer matches the hypotenuse of a right triangle with legs of length 3 and √3. Substitute the values into the Pythagorean theorem: √(3^2 + (√3)^2) = √(9 + 3) = √12. Therefore, this answer matches the given information.