Question 1.

Find the Pythagorean triplets from among the following sets of numbers:

i. 3,4,5

ii. 2,4,5

iii. 4,5,6

iv. 2,6,7

v. 9,40,41

vi. 4,7,8

Solution:

i. 3² = 9,4² = 16, 5² = 25

Now, 9 + 16 = 25

∴ 3² + 42 = 5²

∴ 3, 4 and 5 is a Pythagorean triplet.

ii. 2² = 4, 4² = 16, 5² = 25

But, 4 + 16 ≠ 25

∴ 2² + 4² ≠ 5²

∴ 2, 4 and 5 is not a Pythagorean triplet.

iii. 4² = 16, 5² = 25, 6² = 36

But 16 + 25 ≠ 36

∴ 4² + 5² ≠ 6²

∴ 4, 5 and 6 is not a Pythagorean triplet.

iv. 2² = 4, 6² = 36, 7² = 49

But, 4 + 36 ≠ 49

∴ 2² + 6² ≠ 7²

∴ 2, 6 and 7 is not a Pythagorean triplet.

v. 9² = 81, 40² = 1600,41² = 1681

Now, 81 + 1600 = 1681

∴ 9² + 40² = 41²

∴ 9,40 and 41 is a Pythagorean triplet.

vi. 4² = 16, 7² = 49, 8² = 64

But, 16 + 49 ≠ 64

∴ 4² + 7² ≠ 8²

∴ 4, 7 and 8 is not a Pythagorean triplet.

Question 2.

The sides of some triangles are given below. Find out which ones are right-angled triangles?

i. 8,15,17

ii. 11,12,15

iii. 11,60,61

iv. 1.5, 1.6, 1.7

v. 40, 20, 30

Solution:

i. 8² = 64, 15² = 225, 17² = 289

Now, 64 + 225 = 289

∴ 8² + 15² = 17²

The above expression is of the from (hypotenuse)² = (base)² + (height)²

∴ The sides of lengths 8,15,17 will form a right-angled triangle.

ii. 11² = 121, 12² = 144, 15² = 225

But, 121 + 144 ≠ 225

∴ 11² + 12² ≠ 25²

∴ The above expression is not of the from

(hypotenuse)² = (base)² + (height)²

∴ The sides of lengths 11, 12, 15 will not form a right-angled triangle.

iii. 11² = 121, 60² = 3600, 61² = 3721

Now, 121 +3600 = 3721

∴ 11² + 60² = 61²

∴ The above expression is of the from

(hypotenuse)² = (base)² + (height)²

∴ The sides of lengths 11, 60, 61 will form a right-angled triangle.

iv. 1.5² = 2.25, 1.6² = 2.56, 1.7² = 2.89

But, 2.25 + 2.56 ≠ 2.89

∴ 1.5² + 1.6² ≠ 1.7²

∴ The above expression is not of the from

(hypotenuse)² = (base)² + (height)²

∴ The sides of lengths 1.5, 1.6, 1.7 will not form a right-angled triangle.

v. 40² = 1600, 20² = 400, 30² = 900

But, 400 + 900 ≠ 1600

∴ 20² + 30² ≠ 40²

∴ The above expression is not of the from (hypotenuse)² = (base)² + (height)²

∴ The sides of lengths 40, 20, 30 will not form a right-angled triangle.

**Intext Questions and Activities**

Question 1.

From the numbers 1 to 50, pick out the Pythagorean triplets. (Textbook pg. no. 90)

Solution:

- 3,4,5
- 5,12,13
- 7,24,25
- 8,15,17
- 9,40,41
- 12,35,37
- 20,21,29