Question

How to find a Pythagorean Triplet if one number is given?

Please Answer!

Answer 1

Hey There!

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Q. Find a Pythagorean Triplet if one number is given,

A. First Let's Understand what a P.T is :

P.T is Pythagorean Triplet i.e in a Right angle triangle, All the three Sides of Triangle are referred as P.T

Always They largest number in P.T is Hypotenuse

Umm, It would be difficult to understand if I explain it in this way, Rather let's go for an example....

Suppose Given P.T (Pythagorean Triplet) is 12 and we have to find other P.T then,

NOTE: P.Ts are always in form of

${m}^{2} - 1 \\ 2m \\ {m}^{2} + 1$

Now, Keeping Value of 12 as ${m}^{2} - 1$

Then,${m}^{2} - 1$ = 12 or ${m}^{2}$= 13

Which is not a Whole number

now let's try for ${m}^{2} + 1$= 12

${m}^{2}$ = 11 which is also not a Whole number

Finally, Let's try 2m = 12

m= 6 Which is whole number!!!

Now putting values of m = 6

Case I :${m}^{2} - 1$ {m=6}

36-1 = 35

Case II :${m}^{2} + 1$ {m=6}

36+1 = 37

Therefore P.T are 12,35,37

Some other example of P.T are : 3,4,5

You can try yourself for others and also Verify that 3,4,5 Are P.T or not!

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Hope it Helped!

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Have a Great Day! :)

Answer 2

hey Crystinia hope this helps you