# Sides of triangles are given below. Determine which of them are right triangles. In the 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:**

As we know, in a triangle, if the square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.

(i) (25)^{2} = 625

7^{2} + (24)^{2} = 49 + 576 = 625

Therefore, (25)^{2} = 7^{2} + (24)^{2}

It is a right triangle and length of hypotenuse = 25cm

(ii) 8^{2} = 64

3^{2} + 6^{2} = 9 + 36 = 45

8^{2} ≠ 3^{2} + 6^{2}

It isn't a right triangle.

(iii) (100)^{2} = 10000

(50)^{2} + (80)^{2} = 2500 + 6400 = 8900

(100)^{2} ≠ (50)^{2} + (80)^{2}

It isn't a right triangle.

(iv) (13)^{2} = 169

(12)^{2} + 5^{2} = 144 + 25 = 169

Therefore, (13)^{2} = (12)^{2} + 5^{2}

It is a right triangle and length of hypotenuse = 13cm

Thus (i) and (iv) are right triangles.

**Video Solution:**

## Sides of triangles are given below. Determine which of them are right triangles. In the 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

### NCERT Class 10 Maths Solutions - Chapter 6 Exercise 6.5 Question 1:

Sides of triangles are given below. Determine which of them are right triangles. In the 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

Sides of triangles are given below. Then the right angles of the following are

(i) 7 cm, 24 cm, 25 cm = Right-angled with 25 cm as hypotenuse (ii) 3 cm, 8 cm, 6 cm = Not a right-angled triangle. (iii) 50 cm, 80 cm, 100 cm = Not a right angled triangle. (iv) 13 cm, 12 cm, 5 cm = A right angled triangle with 13 cm as hypotenuse