AMC 12A 2022 Problem 16

A triangular number is a positive integer that can be expressed in the form t_{n}=1+2+3+\cdots+n, for some positive integer n. The three smallest triangular numbers that are also perfect squares are t_{1}=1= 1^{2}, t_{8}=36=6^{2}, and t_{49}=1225=35^{2}. What is the sum of the digits of the fourth smallest triangular number that is also a perfect square?

Answer Choices
A. 6
B. 9
C. 12
D. 18
E. 27