# Which of the following can be the sides of a right triangle?

(i) 2.5 cm, 6.5 cm, 6 cm

(ii) 2 cm, 2 cm, 5 cm

(iii) 1.5 cm, 2cm, 2.5 cm

In the case of right-angled triangles, identify the right angles

**Solution:**

This question is very simple.

Here we need to proceed with the converse of Pythagoras theorem.

Consider the greater side as the hypotenuse and if the square of the hypotenuse is equal to the sum of the square of the other two sides then these are the sides of a right-angled triangle.

(i) (Hypotenuse)^{2 }= (Perpendicular)^{2} + (Base)^{2}

(6.5)^{2} = (6)^{2} +(2.5)^{2}

42.25 = 36+ 6.25

42.25 = 42.25

L.H.S = R.H.S

Therefore, the given sides are of the right-angled triangle.

The right angle lies opposite to the greater side.

(ii) (Hypotenuse)^{2} = (Perpendicular)^{2} + (Base)^{2}

(5)^{2} = (2)^{2} + (2)^{2}

25 = 4 + 4

25 ≠ 8

Therefore, the given sides are not of a right- angled triangle.

(iii) (Hypotenuse)^{2} = (Perpendicular)^{2} + (Base)^{2}

(2.5)^{2} = (2)^{2} + (1.5)^{2}

6.25 = 4 + 2.25

6.25 = 6.25

L.H.S = R.H.S

Therefore, the given sides are of a right-angled triangle.

The right angle lies on the opposite to the greater side.

**Video Solution:**

## Which of the following can be the sides of a right triangle? (i) 2.5 cm, 6.5 cm, 6 cm (ii) 2 cm, 2 cm, 5 cm (iii) 1.5 cm, 2cm, 2.5 cm. In the case of right-angled triangles, identify the right angles

### NCERT Solutions for Class 7 Maths - Chapter 6 Exercise 6.5 Question 4

Which of the following can be the sides of a right triangle? (i) 2.5 cm, 6.5 cm, 6 cm (ii) 2 cm, 2 cm, 5 cm. (iii) 1.5 cm, 2cm, 2.5 cm. In the case of right-angled triangles, identify the right angles

(i) 2.5 cm, 6.5 cm, 6 cm follows the Pythagoras theorem, so will form a right-angled triangle (ii) 2 cm, 2 cm, 5 cm do not follow the Pythagoras theorem, so will not form a right-angled triangle (iii) 1.5 cm, 2cm, 2.5 cm follows the Pythagoras theorem, so will form a right-angled triangle