**CBSE NCERT Solutions Chapter 6 Triangles Exercise 6.5 Question 1**

**1.** Sides of triangles are given below. Determine which of them are right triangles. In case of a right triangle, write the length of its hypotenuse.

(i) 7 cm, 24 cm, 25 cm

(ii) 3 cm, 8 cm, 6 cm

(iii) 50 cm, 80 cm, 100 cm

(iv) 13 cm, 12 cm, 5 cm

**Solution (i)**

7 cm, 24 cm, 25 cm

To check if these are sides of right triangle, we pick two shorter sides and find sum of their squares. If, sum of their squares is equal to square of largest side then these all are sides of right angled triangle. If, it is a right angled triangle then the largest length available would be the length of hypotenuse.

It means by pythagoras theorem, we can say that these are sides of right angled triangle.

Length of hypotenuse is 25 cm.

**Solution (ii)**

3 cm, 8 cm, 6 cm

To check if these are sides of right triangle, we pick two shorter sides and find sum of their squares. If, sum of their squares is equal to square of largest side then these all are sides of right angled triangle. If, it is a right angled triangle then the largest length available would be the length of hypotenuse.

It does not verify pythagoras theorem which means these are not sides of right angled triangle.

**Solution (iii)**

50 cm, 80 cm, 100 cm

To check if these are sides of right triangle, we pick two shorter sides and find sum of their squares. If, sum of their squares is equal to square of largest side then these all are sides of right angled triangle. If, it is a right angled triangle then the largest length available would be the length of hypotenuse.

It does not verify pythagoras theorem which means these are not sides of right angled triangle.

**Solution (iv)**

13 cm, 12 cm, 5 cm

It means by pythagoras theorem, we can say that these are sides of right angled triangle.

Length of hypotenuse is 13 cm.