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?

\text{(A)}\;6

\text{(B)}\;9

\text{(C)}\;12

\text{(D)}\;18

\text{(E)}\;27