# Video: Pack 2 β’ Paper 1 β’ Question 3

Pack 2 β’ Paper 1 β’ Question 3

02:01

### Video Transcript

Triangle πππ has a perimeter of 30 centimeters. ππ equals 12 centimeters. ππ equals 13 centimeters. Determine by calculation where triangle πππ is a right-angled triangle.

The perimeter of any triangle is the sum of its three lengths. In this case, ππ plus ππ plus ππ is equal to 30 as the perimeter is 30 centimeters. Substituting in the length of ππ and ππ gives us 12 plus 13 plus ππ 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 ππ of five centimeters.

As we now know all three lengths of the triangle, we can check whether it is right angled by using Pythagorasβs 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 ππ and ππ 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 ππ. Therefore, we need to square 13. 13 squared is also equal to 169.

We can, therefore, say yes, πππ is a right-angled triangle as it satisfies Pythagorasβs theorem. Any triangle that satisfies Pythagorasβs theorem will be right angled.