In this video, let's discuss an important property about Pythagorean triplets.
Now let's try to understand what we mean by the Göring triplets.
Let's have a right angle triangle ABC over here.
Now let's take the sides as five, three and four.
And you will see that five squared is equal to three squared plus four square.
Right y five square is twenty five.
Square is nine and four square is sixteen nine plus sixteen gives you twenty five.
And we have seen that this is true because of Pythagoras Theorem.
Right now, the set of numbers five, three and four because they follow this pattern are called Pythagoras
Intraplate.
All right.
Now the interesting property about Pythagoras triplets is that if you take any Pythagoras and you multiply
it with the number, you will get another by the triplet.
For example, let's take this Pythagoras triplet and multiply it throughout with two to five.
And the two gives you ten.
Three in the two gives you six and four and the two gives you eight.
Now you will see that 10 square is equal to six squared plus eight square.
Ten square gives you hundred six square gives you thirty six and eight square gives you sixty four.
Well this is true and this is another by the intraplate.
Now let's multiply five, three, four with three we will get 15, nine and 12 and you'll see that this
is also a Pythagoras triplet that is five.
Fifteen square is equal to nine squared plus 12 square.
Similarly, if you multiply five, three, four with four, you will get twenty 12 and 16.
And that is also a Pythagoras intraplate.
So this is a very useful property.
You take any by intraplate and you multiply it with the number or you divide it with the number, you
will get another Pythagorean triplet.