(C) Let the three numbers be $3x$,$4x$,and $5x$.According to the problem,the sum of their squares is $1250$.Therefore,$(3x)^2 + (4x)^2 + (5x)^2 = 1250

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(C) Let the three numbers be $3x$,$4x$,and $5x$.According to the problem,the sum of their squares is $1250$.Therefore,$(3x)^2 + (4x)^2 + (5x)^2 = 1250$.$9x^2 + 16x^2 + 25x^2 = 1250$.$50x^2 = 1250$.$x^2 = \frac{1250}{50} = 25$.$x = 5$.The sum of the numbers is $3x + 4x + 5x = 12x$.Substituting the value of $x$,we get $12 \times 5 = 60$.