SQL select advance - Type of Triangle (make use of CASE WHEN THEN ELSE END)

Problem

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:

• Not A Triangle: The given values of A, B, and C don't form a triangle.
• 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.

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 .

Answer

select
    CASE
    when(a+b>c) and (a+c>b) and (b+c>a)then
        case
            when(a=b) and (b=c) and (c=a) then 'Equilateral'
            when (a=b)or (b=c) or (a=c)then 'Isosceles'  
            else 'Scalene'
        end
    else 'Not A Triangle'
    end
from TRIANGLES