Type of Triangle

Write a query identifying the type of each record in the TRIANGLES table using its three side lengths. Output one of the following statements for each record in the table:

• Equilateral: It's a triangle with  sides of equal length.
• Isosceles: It's a triangle with  sides of equal length.
• Scalene: It's a triangle with  sides of differing lengths.
• Not A Triangle: The given values of A, B, and C don't form a triangle.

Input Format

The TRIANGLES table is described as follows:

Each row in the table denotes the lengths of each of a triangle's three sides.

Sample Input

Sample Output

Isosceles
Equilateral
Scalene
Not A Triangle

Explanation

Values in the tuple  form an Isosceles triangle, because . 
Values in the tuple  form an Equilateral triangle, because . Values in the tuple form a Scalene triangle, because . 
Values in the tuple  cannot form a triangle because the combined value of sides  and  is not larger than that of side .

SOLUTION :

SELECT CASE WHEN A + B > C AND A+C>B AND B+C>A THEN 

CASE WHEN A = B AND B = C THEN 'Equilateral' 

WHEN A = B OR B = C OR A = C THEN 'Isosceles' 

WHEN A != B OR B != C OR A != C THEN 'Scalene' 

END ELSE 'Not A Triangle' END FROM TRIANGLES;