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AnswerQuestion Answers for Class 12Class 12 BiologyClass 12 ChemistryClass 12 EnglishClass 12 MathsClass 12 PhysicsClass 12 Social ScienceClass 12 Business StudiesClass 12 EconomicsQuestion Answers for Class 11Class 11 EconomicsClass 11 Computer ScienceClass 11 BiologyClass 11 ChemistryClass 11 EnglishClass 11 MathsClass 11 PhysicsClass 11 Social ScienceClass 11 AccountancyClass 11 Business StudiesQuestion Answers for Class 10Class 10 ScienceClass 10 EnglishClass 10 MathsClass 10 Social ScienceClass 10 General KnowledgeQuestion Answers for Class 9Class 9 General KnowledgeClass 9 ScienceClass 9 EnglishClass 9 MathsClass 9 Social ScienceQuestion Answers for Class 8Class 8 ScienceClass 8 EnglishClass 8 MathsClass 8 Social ScienceQuestion Answers for Class 7Class 7 ScienceClass 7 EnglishClass 7 MathsClass 7 Social ScienceQuestion Answers for Class 6Class 6 ScienceClass 6 EnglishClass 6 MathsClass 6 Social ScienceQuestion Answers for Class 5Class 5 ScienceClass 5 EnglishClass 5 MathsClass 5 Social ScienceQuestion Answers for Class 4Class 4 ScienceClass 4 EnglishClass 4 MathsWhat are the Pythagorean triples whose one member is 20?A. $20,97,99$B. $20,99,101$C. $20,197,199$D. $20,199,201$AnswerVerified559.2k+ viewsHint: According to the question given in the question we have to determine the Pythagorean triples whose one member is 20. So, first of all we have to understand about the Pythagorean triplet which is explained as below:Pythagorean triplet: Pythagorean triplet is consist of a three positive integers as x, y, and z such that ${x^2} + {y^2} = {z^2}$and when the sides of a triangle are Pythagorean triplet then triangle is a right angled triangle.Now, first of all as we know that for any natural number $n > 1$and $2n,{n^2} - 1,{n^2} + 1$forms a Pythagorean triplet.Now, we have to obtain the values of $2n,{n^2} - 1,{n^2} + 1$which are the required Pythagorean triplets.Complete step-by-step solution:Step 1: First of all as we know for any natural number $n > 1$ the Pythagorean triplets are:$ \Rightarrow 2n,{n^2} - 1,{n^2} + 1$……………(1)Step 2: Now, we can obtain the first triplet by substituting the value in triplet ${n^2} - 1$. Hence, $ \Rightarrow {n^2} - 1 = 20 \\ \Rightarrow {n^2} = 21.................(2) $Step 3: Same as the step 2 we can obtain the first triplet by substituting the value in triplet${n^2} + 1$. Hence,$ \Rightarrow {n^2} + 1 = 20 \\ \Rightarrow {n^2} = 19.................(3) $Step 4: Same as the step 2 we can obtain the first triplet by substituting the value in triplet$2n$. Hence,$ \Rightarrow 2n = 20 \\ \Rightarrow n = \dfrac{{20}}{2} \\ \Rightarrow n = 10 $Step 5: Now, we have to substitute the value of n in the triplet as${n^2} - 1$. Hence, $ = {10^2} - 1 \\ = 100 - 1 \\ = 99 $Step 5: Now, same as the step 5 we have to substitute the value of n in the triplet as${n^2} + 1$. Hence,$ = {10^2} + 1 \\ = 100 + 1 \\ = 101 $Hence, we have obtained the Pythagorean triples whose one member is 20 are $20,99,101$. Therefore option (B) is correct.Note: A Pythagorean triplet always consists of all even numbers, or two odd numbers and an even number. Pythagorean triplet is consist of a three positive integers as x, y, and z such that ${x^2} + {y^2} = {z^2}$ and when the sides of a triangle are Pythagorean triplet then triangle is a right angled triangle.Recently Updated PagesMaster Class 11 Accountancy: Engaging Questions & Answers for SuccessMaster Class 11 Science: Engaging Questions & Answers for SuccessMaster Class 11 Business Studies: Engaging Questions & Answers for SuccessMaster Class 11 English: Engaging Questions & Answers for SuccessMaster Class 11 Computer Science: Engaging Questions & Answers for SuccessMaster Class 9 General Knowledge: Engaging Questions & Answers for SuccessMaster Class 11 Accountancy: Engaging Questions & Answers for SuccessMaster Class 11 Science: Engaging Questions & Answers for SuccessMaster Class 11 Business Studies: Engaging Questions & Answers for SuccessMaster Class 11 English: Engaging Questions & Answers for SuccessMaster Class 11 Computer Science: Engaging Questions & Answers for SuccessMaster Class 9 General Knowledge: Engaging Questions & Answers for Success

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