Pythagorean Triplet
Pythagorean Triplet
Property :For any natural number m greater than 1 the Pythagorean triplet are represented as
Proof: In order to prove that is a Pythagorean triplet, it is sufficient to prove that
We have,
Hence, is Pythagorean triplet for any natural number m > 1.
Remark: If m and n are relatively prime natural numbers such that m > n and exactly one of them is even and other is odd, then is a primitive Pythagorean triple.
Here, the word primitive means that the three numbers contain no common factor.
Illustration: Write a Pythagorean triplet whose one member is:
(i) 6 (ii) 18
Solution: For any natural number m > 1, we have
as a Pythagorean triplet.
(i) Here,
and
Hence the pythagorean triplet is (6,8,10)
(ii) Here,
and
Hence the pythagorean triplet is (18,80,82)
Which one of the triplets given below is not Pythagorean triplet ?
| |||
| Right Option : A | |||
| View Explanation | |||
Check whether (6,32,34) is a pythagorean triplet or not | |||
| Right Option : B | |||
| View Explanation | |||
What will be the length of third side of a right angled triangle whose hypotenuse is 5cm and one of the side is 3 cm? | |||
| Right Option : C | |||
| View Explanation | |||
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