### Video Transcript

Triangle πππ has a perimeter of
30 centimeters. ππ equals 12 centimeters. ππ equals 13 centimeters. Determine by calculation where
triangle πππ is a right-angled triangle.

The perimeter of any triangle is
the sum of its three lengths. In this case, ππ plus ππ plus
ππ is equal to 30 as the perimeter is 30 centimeters. Substituting in the length of ππ
and ππ gives us 12 plus 13 plus ππ is equal to 30. 12 plus 13 is equal to 25. Finally, subtracting 25 from both
sides of this equation gives us a length of ππ of five centimeters.

As we now know all three lengths of
the triangle, we can check whether it is right angled by using Pythagorasβs
theorem. This states that in right-angled
triangles π squared plus π squared is equal to π squared, where π is the
hypotenuse or longest side of the right-angled triangle.

Squaring the two shorter sides ππ
and ππ gives us 12 squared plus five squared. 12 squared is equal to 144 and five
squared is equal to 25. Adding these two values give us
169. The hypotenuse is ππ. Therefore, we need to square
13. 13 squared is also equal to
169.

We can, therefore, say yes, πππ
is a right-angled triangle as it satisfies Pythagorasβs theorem. Any triangle that satisfies
Pythagorasβs theorem will be right angled.