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Pythagorean Triplet

Square and Square Root I - Concepts

Perfect Square

Square of Number 1-50

Square Root Using Prime Factorization

General Properties of Squares

Properties of Square - Based on Ending Digits

Properties of Square - Unit Digit of Square

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Pythagorean Triplet

Number Between Square Numbers

Properties of Square - Based on Pattern

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Concept Explanation

Pythagorean Triplet

Property :For any natural number m greater than 1 the Pythagorean triplet are represented as

$(2m,m^{2}-1,m^{2}+1)$

Proof: In order to prove that $(2m,m^{2}-1,m^{2}+1)$ is a Pythagorean triplet, it is sufficient to prove that

$(2m)^{2}+(m^{2}-1)^{2}=(m^{2}+1)^{2}$

We have, $(2m)^{2}+(m^{2}-1)^{2}=4m^{2}+m^{4}-2m^{2}+1^{2}$

$=m^{4}+2m^{2}+1^{2}$

$=(m^{2}+1)^{2}$

Hence, $(2m,m^{2}-1,m^{2}+1)$ 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 $(2mn,m^{2}-n^{2},m^{2}+n^{2})$ 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

$2m,m^{2}-1,m^{2}+1$ as a Pythagorean triplet.

(i) Here,

$2m=6Rightarrow m=3.$

$therefore ;m^{2}-1=3^{2}-1=9-1=8$ and $m^{2}+1=3^{2}+1=9+1=10$

Hence the pythagorean triplet is (6,8,10)

(ii) Here,

$2m=18Rightarrow m=9.$

$therefore ;m^{2}-1=9^{2}-1=81-1=80$ and $m^{2}+1=9^{2}+1=81+1=82$

Hence the pythagorean triplet is (18,80,82)

Sample Questions

(More Questions for each concept available in Login)

Question : 1

Check which of the following is not a pythagorean triplet
A. (12,35,37)	B. (12,33,37)	C. (12,34,36)	D. (12,34,37)
Right Option : A
View Explanation

Question : 2

Choose a Pythagorean triplet whose one member is 4.
A. (3,4,5)	B. (7,12,5)	C. (5,10,13)	D. (5,18,13)
Right Option : A
View Explanation

Question : 3

(6,8,10) and (5,12,13) are __________________
A. Both are Pythagorean triplets		B. None of the both is Pythagorean triplet
C. First is Pythagorean triplet while second is not		D. Second is Pythagorean tripletwhile first is not
Right Option : A
View Explanation

Chapters

Exponents and Power II

Introduction to Trigonometry II

Introduction to Trigonometry I

Linear Equations in One Variable II

Linear Equations in One Variable I

Cube and Cube Roots

Square and Square Root II

Square and Square Root I

Rational Numbers II

Rational Numbers I

Mensuration I

Exponents and Power I

Direct and Inverse Variation II

Direct and Inverse Variation I

Algebraic Expressions

Comparing Quantities III

Comparing Quantities II

Comparing Quantities I

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Attention !!!!!

Pythagorean Triplet

Pythagorean Triplet

Property :For any natural number m greater than 1 the Pythagorean triplet are represented as

Students / Parents Reviews [10]

Shreya Shrivastava

Eshan Arora

Ayan Ghosh

Hiya Gupta

Manish Kumar

Yatharthi Sharma

Prisha Gupta

Cheshta

Om Umang

Barkha Arora