Question

If $a$, $b$, $c$ are sides of a triangle and $a^2 + b^2 = c^2$, name the type of triangle:

• A. Obtuse angled triangle
• B. Acute angled triangle
• C. Right angled triangle
• D. Equilateral triangle

Hint:

If the sum of squares of two sides equals the square of the third side, the triangle is right-angled.

Answer 1

The Correct Option is C

Step 1: Recall the Pythagoras Theorem.
According to the Pythagoras theorem, for a right-angled triangle having sides $a$, $b$ (legs), and $c$ (hypotenuse), the relation is given by:
\[ a^2 + b^2 = c^2 \]
Step 2: Compare with the given condition.
The question states that $a^2 + b^2 = c^2$. Hence, this satisfies the condition of the Pythagoras theorem.
Step 3: Conclusion.
Therefore, the triangle is a Right-angled triangle.