Question

Check whether given sides are the sides of right – angled triangles, using Pythagoras theorem,

1. 8, 15, 17
2. 12, 13, 15
3. 30, 40, 50
4. 9, 40, 41
5. 24, 45, 51

Answer 1

1. 8, 15, 17

Take a = 8,

b = 15 and

c = 17

Now a² + b² = 8² + 15² = 64 + 225 = 289

17² = 289 = c²

∴ a² + b² = c²

By the converse of Pythagoras theorem, the triangle with given measures is a right angled triangle.

Answer:

yes.

2. 12, 13, 15

Take a = 12

b = 13 and

c = 15

Now a² + b² = 12² + 13² = 144 + 169 = 313

15² = 225 ≠ 313

By the converse of Pythagoras theorem, the triangle with given measures is not a right angled triangle.

Answer:

No.

3. 30, 40, 50

Take a = 30

b = 40 and

c = 50

Now a² + b² = 30² + 40² = 900 + 1600 = 2500

c² = 50² = 2500

∴ a² + b² = c²

By the converse of Pythagoras theorem, the triangle with given measures is a right angled triangle.

Answer:

yes.

4. 9, 40, 41

Take a = 9

b = 40 and

c = 41

Now a² + b² = 9² + 40² = 81 + 1600= 1681

c² = 41² = 1681

∴ a² + b² = c²

By the converse of Pythagoras theorem, the triangle with given measures is a right angled triangle.

Answer:

Yes.

5. 24, 45, 51

Take a = 24

b = 45 and

c = 51 Now

a² + b² = 24² + 45² = 576 + 2025 = 2601

c² = 51² = 2601

a² + b² = c²

By the converse of Pythagoras theorem, the triangle with given measure is a right angled triangle.

Answer:

Yes.