Question

The sides of certain triangles are given below. Determine which of them are right triangles.

a = 9 cm, b = 16 cm and c = 18 cm

Answer 1

Given: a = 9 cm, b = 16 cm, c = 18 cm.

Step-wise calculation: For a triangle to be right-angled, the square of the largest side (hypotenuse) must equal the sum of the squares of the other two sides (Pythagoras' theorem).

1. Identify largest side: c = 18 is largest.

2. Compute a² + b² 

= 9² + 16² 

= 81 + 256

= 337

3. Compute c² = 18²

= 324

4. Compare: 337 ≠ 324, so c² ≠ a² + b². 

For completeness: if 16 were hypotenuse, 9² + 18² = 405 ≠ 256;

if 9 were hypotenuse, 16² + 18² = 580 ≠ 81.

The triangle with sides 9 cm, 16 cm and 18 cm is NOT a right triangle.