Type of Triangle

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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 (20,20,23) form an Isosceles triangle, because A=B.

Values in the tuple (20,20,20) form an Equilateral triangle, because A=B=C.

Values in the tuple (20,21,22) form a Scalene triangle, because A≠B≠C.

Values in the tuple (13,14,30) cannot form a triangle because the combined value of sides A and B is not larger than that of side C.

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

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