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:

• 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 .

Query:
select
case
when (a+b)<=c or (a+c)<=b or (b+c)<=a  then 'Not A Triangle'
when a=b and b=c then 'Equilateral'
when (a=b and b<>c) or (b=c and a<>c) or (a=c and c<>b)  then 'Isosceles'
else    'Scalene'
end
from Triangles;