# 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:**

We will be proceeding with the converse of Pythagoras theorem to solve this question.

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} = 42.25

(6)^{2} +(2.5)^{2} = 36 + 6.25

42.25 = 42.25

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

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

The right angle lies opposite to the greater side that is 6.5 cm.

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

(5)^{2} = 25

(2)^{2} + (2)^{2} = 4 + 4 = 8

25 ≠ 8

Thus, (5)^{2} ≠ (2)^{2} + (2)^{2}

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

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

(2.5)^{2} = 6.25

(2)^{2} + (1.5)^{2} = 4 + 2.25

6.25 = 6.25

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

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

The right angle lies opposite to the greater side that is 2.5 cm.

**ā Check: **NCERT Solutions for Class 7 Maths Chapter 6

**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

**Summary:**

(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

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