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    SQL Server Solution-

    SELECT CASE WHEN A + B > C AND B + C > A AND C + A > B THEN CASE
    WHEN (A = B) AND (B = C) THEN 'Equilateral' WHEN (A = B) OR (B = C) OR (A = C) THEN 'Isosceles' ELSE 'Scalene' END ELSE 'Not A Triangle' END FROM TRIANGLES