A triangle has sides of \( 6 \mathrm{~cm}, 8 \mathrm{~cm} \) and 9 cm . Is it right-angled? Yes No

No, the triangle is not right-angled. **Explanation:** To determine if a triangle with sides of 6 cm, 8 cm, and 9 cm is right-angled, we can use the Pythagorean theorem. The theorem states that in a right-angled triangle, the square of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides. Let's identify the longest side: - Longest side (hypotenuse): 9 cm - Other two sides: 6 cm and 8 cm Now, apply the Pythagorean theorem: \[ \text{Hypotenuse}^2 = \text{Side}_1^2 + \text{Side}_2^2 \] \[ 9^2 = 6^2 + 8^2 \] \[ 81 = 36 + 64 \] \[ 81 \neq 100 \] Since \(81 \neq 100\), the triangle does not satisfy the Pythagorean theorem and therefore is **not** a right-angled triangle.