Question

If the sides of a triangle are 3 cm, 4 cm and 5 cm, then the triangle will be:

• A. right angle triangle
• B. acute angle triangle
• C. obtuse angle triangle
• D. triangle is not possible

Hint:

For a triangle to be a right-angle triangle, the square of the longest side should equal the sum of the squares of the other two sides.

Answer 1

The Correct Option is A

Step 1: Check the Pythagoras theorem.
For a triangle with sides \( a \), \( b \), and \( c \) (where \( c \) is the hypotenuse), it will be a right-angle triangle if it satisfies the Pythagoras theorem: \[ a^2 + b^2 = c^2 \]
Step 2: Apply the sides of the triangle.
The given sides are 3 cm, 4 cm, and 5 cm. Let’s assume \( c = 5 \) cm (the longest side), and \( a = 3 \) cm, \( b = 4 \) cm. Now, check the Pythagoras theorem: \[ 3^2 + 4^2 = 9 + 16 = 25 \] \[ 5^2 = 25 \] Since both sides are equal, the triangle satisfies the Pythagoras theorem, so it is a right-angle triangle.
Step 3: Conclusion.
Therefore, the correct answer is (A) right angle triangle.