### Video Transcript

Is this a right-angled
triangle?

The triangle shown has lengths four
centimetres, six centimetres, and seven centimetres. If the triangle is right-angled, it
must satisfy Pythagoras’s theorem. 𝑎 squared plus 𝑏 squared equals
𝑐 squared, where the length 𝑐 is the hypotenuse or longest side of the
triangle.

We need to work out is four squared
plus six squared equal to seven squared. Four squared is equal to 16. Six squared is equal to 36. On the right-hand side, seven
squared is equal to 49. 16 plus 36 is equal to 52. This is not equal to 49.

Therefore, the triangle is not
right-angled. A triangle with lengths four
centimetres, six centimetres, and seven centimetres will not be right-angled as it
does not satisfy Pythagoras’s theorem.