7. Given that $\triangle A B C$ is a right-angled triangle with integer sides, $B C$ is the hypotenuse, and $2 A C=B C+A B$. Which of the following numbers could be a side length of this triangle ( ).
(A) 31
(B) 41
(C) 51
(D) 61
7. Solution From the given, we have
$$
\left\{\begin{array}{l}
B C^{2}=A C^{2}+A B^{2}, \\
2 A C=B C+A B .
\end{array}\right.
$$

By solving the equations, we get
$$
B C: A C: A B=5: 4: 3 \text{. }
$$

Therefore, the sides of $\triangle A B C$ are multiples of 5, 4, and 3. Among the four options, only 51 is a multiple of 3, while the other three numbers 31, 41, and 61 are neither multiples of 3, 4, nor 5.
Choose C.