Step-by-step Solution:

Explanation:
Let the two sides of the triangle be 'a' and 'b', and the third side be 'z'. Given:
Sum of two sides: a² + b²
Product of two sides: 2ab cos C
Equation: z² = a² + b² - 2ab cos C

From the third given equation, we expand using the difference of squares formula:
(z)² = (a - b)² + 2ab (1 - cos C)

Substitute the values of a² + b² and 2ab cos C from the first two conditions into this equation:
z² = a² + b² - 2ab cos C

Rearrange the terms to isolate z²:
z² > a² + b²

Compare with the cosine rule:
z² = a² + b² - 2ab cos C
Rearranged:
cos C = (a² + b² - z²) / (2ab)

Since a and b are positive,
cos C < 0

For cos C < 0, the angle C must be greater than 90°. Since one angle of the triangle is greater than 90°, the triangle is an obtuse-angled triangle.