Question

With usual notations, if in \( \triangle ABC \), \( s \) is the semi-perimeter and \( (s - a)(s - b) = (s - c) \), then \( \triangle ABC \) is

• A. an equilateral triangle
• B. an obtuse angle triangle
• C. a right angled triangle
• D. an acute angle triangle

Hint:

For a right-angled triangle, the semi-perimeter conditions satisfy \( (s - a)(s - b) = (s - c) \).

Answer 1

The Correct Option is C

Step 1: Use the given condition.
The given condition is \( (s - a)(s - b) = (s - c) \), which is a known property of right-angled triangles. This condition holds specifically for a right-angled triangle.
Step 2: Conclusion.
Thus, \( \triangle ABC \) is a right-angled triangle, corresponding to option (C).