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)
What is the length of the diagonal of a rectangle having dimensions 3 cm and 4cm ? | |||
| Right Option : A | |||
| 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 | |||
Choose a Pythagorean triplet whose one member is 4. | |||
| Right Option : A | |||
| View Explanation | |||
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