Question

find a Pythagorean triplets whose one member is 20.

Answer 1

hey mate,,,

here's ur answer...

to find -- Pythagorean triplets whose one member is 20.


answer --
Pythagorean Triplet =2m , m+1 , m-1 

2m=20 
m=20/2 
m=10 

m²+1=10²+1=100+1=101 
m²-1=10²-1=100-1=99 

Members of the Pythagorean triplets are 20 , 101 ,99...


hope it is helpful.....

Answer 2

Concept Introduction:-

A Pythagorean triplet are made up of $3$ positive integral a and b and c.

Given Information:-

We have been given that Pythagorean triplets whose one member is $20$.

To Find:-

We have to find that a Pythagorean triplets whose one member is $20$.

Solution:-

According to the problem

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 the 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.

First of all as we know for any natural number  $n > 1$ the Pythagorean triplets are: ⇒$2n,n^{2}-1,n^{2}+1$......$(1)$

Now, we can obtain the first triplet by substituting the value in a triplet $n^2-1$. Hence,

$n^2-1=20\\n=21$.................$(2)$

we can obtain the first triplet by substituting the value in triplet $n^2+1$. Hence,

$n^2+1=20\\n^2=19$.................$(3)$

we can obtain the first triplet by substituting the value in triplet $2n$. Hence,

$2n=20\\n=\frac{20}{2}\\n=10$

Now, we have to substitute the value of n in the triplet as $n^2-1$. Hence,

$=102-1=100-1=99$

we have to substitute the value of n in the triplet as $n^2+1$. Hence,

$=102+1=100+1=101$

Hence, we have obtained the Pythagorean triples whose one member is $20$ are $20,99,101$.

Final Answer:-

We have obtained the Pythagorean triples whose one member is $20$ are $20,99,101$.

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