Type of Triangle - Solution & Explanation

This approach involves checking if the given sides can form a triangle using the triangle inequality theorem. If they can form a triangle, we check the equality of the side lengths to determine the type of triangle. The triangle inequality requires that the sum of the lengths of any two sides must be greater than the length of the remaining side. Once we establish that the sides form a valid triangle, we compare the sides to classify the triangle as equilateral, isosceles, or scalene.

Here's how we can implement this:

• Check the triangle inequality theorem: If any sum of two sides is not greater than the third, it's not a triangle.
• Check side lengths: If all sides are equal, return 'equilateral'. If two sides are equal, return 'isosceles'. Otherwise, return 'scalene'.

In this C solution, we first check whether the inputs satisfy the triangle inequality theorem using a series of conditional checks. If any two sides do not sum to be greater than the third side, we return "none". Otherwise, we then check for the equality of sides to find out if the triangle is equilateral, isosceles, or scalene.

This approach involves sorting the sides of the triangle first to simplify the comparison process. Sorting will guarantee that a <= b <= c, allowing us to simply verify the triangle inequality with a + b > c. Once sorted, determining the type of triangle becomes straightforward with equality checks.

Steps involved:

• Sort the sides, ensuring a <= b <= c.
• Apply a simplified triangle inequality check using a + b > c.
• Classify the type of triangle by comparing the sorted sides.

We employ the qsort function to sort the array in ascending order. This simplifies the inequality checking to a single condition: if nums[0] + nums[1] > nums[2] holds true, a triangle is possible. Side equality checks are performed on the sorted array to determine the triangle type, leveraging the sorted order for simplicity.