Write a Pythagorean triplet whose one member is:
(i) 6 (ii) 14 (iii) 16 (iv) 18
Solution:
For any natural number 'm' where m > 1, we have (2m)2 + (m2 - 1)2 = (m2 + 1)2.
So, 2m, m2 - 1 and m2 + 1 forms a Pythagorean triplet
(i) If we take m2 + 1 = 6,
m2 = 5
The value of m will not be an integer.
If we take m2 - 1 = 6
m2 = 7
Again, the value of m will not be an integer.
Let 2m = 6
m = 6/2 = 3
m2 - 1 = (3)2 - 1
= 9 - 1 = 8
m2 + 1 = (3)2 + 1
= 9 + 1 = 10
Therefore, Pythagorean triplets are 6, 8 and 10
(ii) If we take m2 + 1 = 14,
m2 = 13
The value of the m will not be an integer.
If we take m2 - 1 = 14
m2 = 15
Again, the value of m will not be an integer.
Let 2m = 14
Thus, m = 7
m2 - 1 = 72 - 1
= 49 - 1 = 48
m2 + 1 = 72 + 1
= 49 + 1 = 50
Therefore, 14, 48, 50 are Pythagorean triplets.
(iii) If we take m2 + 1 = 16,
m2 = 15
The value of the m will not be an integer.
If we take m2 - 1 = 16
m2 = 17
The value of the m will not be an integer
Let 2m = 16
Thus, m = 8
m2 - 1 = 82 - 1
= 64 - 1 = 63
m2 + 1 = 82 + 1
= 64 + 1 = 65
Therefore, 16, 63, 65 are Pythagorean triplets.
(iv) If we take m2 + 1 = 18,
m2 = 17
The value of the m will not be an integer.
If we take m2 - 1 = 18
m2 = 19
Again, the value of m will not be an integer.
Let 2m = 18
Thus, m = 9
m2 - 1 = 92 - 1
= 81 - 1 = 80
m2 + 1 = 92 + 1
= 81 + 1 = 82
Therefore, 18, 80, 82 are Pythagorean triplets.
☛ Check: NCERT Solutions for Class 8 Maths Chapter 6
Video Solution:
Write a Pythagorean triplet whose one member is: (i) 6 (ii) 14 (iii) 16 (iv) 18
NCERT Solutions for Class 8 Maths Chapter 6 Exercise 6.2 Question 2
Summary:
The Pythagorean triplets for the given questions are (i) 6, 8 and 10, (ii) 14, 48 and 50. (iii) 16, 63, 65 and (iv) 18, 80, 82
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