Decide whether the triangle with side 9m ,11m and 14m is a right angle triangle ?

To determine if the triangle with sides 9m, 11m, and 14m is a right angle triangle, we can use the Pythagorean theorem.

According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let's check if this is true for the given triangle:

9^2 + 11^2 = 81 + 121 = 202
14^2 = 196

Since 202 is not equal to 196, the triangle with sides 9m, 11m, and 14m is not a right angle triangle.

Theorem:

In a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

Given:

Sides of the triangle: 9m, 11m, 14m

Calculations:

- Square of the length of the longest side (hypotenuse): 14² = 196
- Sum of the squares of the lengths of the other two sides: 9² + 11² = 81 + 121 = 202

Comparison:

196 ≠ 202

Conclusion:

Since the square of the length of the hypotenuse is not equal to the sum of the squares of the lengths of the other two sides, the given triangle is not a right angle triangle.