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:

We know that 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. (Pythagoras theorem)

(i) (25)² = 625

7² + (24)² = 49 + 576 = 625

Therefore, (25)² = 7² + (24)²

It is a right triangle and length of hypotenuse = 25 cm [Since hypotenuse is the longest side of a right triangle]

(ii) 8² = 64

3² + 6² = 9 + 36 = 45

8² ≠ 3² + 6²

Therefore, it's not a right triangle.

(iii) 100² = 10000

50² + 80² = 2500 + 6400 = 8900

100² ≠ 50² + 80²

Therefore, it's not a right triangle.

(iv) 13² = 169

12² + 5² = 144 + 25 = 169

Therefore, 13² = 12² + 5²

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

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

☛ Check: NCERT Solutions Class 10 Maths Chapter 6

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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

Summary:

Sides of triangles are given below. We have, (i) 7 cm, 24 cm, 25 cm: Right-angled triangle 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: Right-angled triangle with 13 cm as hypotenuse.

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