Question

Find whether the given sides of the triangle form a right-angled triangle or not:

8 cm, 9 cm and 12 cm

Answer 1

Given: Sides = 8 cm, 9 cm, 12 cm.

Step-wise calculation:

1. Identify the largest side possible hypotenuse:

12 cm

2. Square the largest side:

12² = 144

3. Square and add the other two sides:

8² + 9²

= 64 + 81

= 145

4. Compare:

12² = 144 ≠ 145

= 8² + 9²   ...(Difference = 1)
So, the Pythagorean equality does not hold; since 12² < 8² + 9², the triangle is acute.

The sides 8 cm, 9 cm and 12 cm do NOT form a right-angled triangle they form an acute triangle.