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In this video, let's discuss an important property about Pythagorean triplets.

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Now let's try to understand what we mean by the Göring triplets.

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Let's have a right angle triangle ABC over here.

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Now let's take the sides as five, three and four.

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And you will see that five squared is equal to three squared plus four square.

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Right y five square is twenty five.

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Square is nine and four square is sixteen nine plus sixteen gives you twenty five.

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And we have seen that this is true because of Pythagoras Theorem.

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Right now, the set of numbers five, three and four because they follow this pattern are called Pythagoras

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Intraplate.

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All right.

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Now the interesting property about Pythagoras triplets is that if you take any Pythagoras and you multiply

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it with the number, you will get another by the triplet.

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For example, let's take this Pythagoras triplet and multiply it throughout with two to five.

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And the two gives you ten.

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Three in the two gives you six and four and the two gives you eight.

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Now you will see that 10 square is equal to six squared plus eight square.

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Ten square gives you hundred six square gives you thirty six and eight square gives you sixty four.

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Well this is true and this is another by the intraplate.

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Now let's multiply five, three, four with three we will get 15, nine and 12 and you'll see that this

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is also a Pythagoras triplet that is five.

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Fifteen square is equal to nine squared plus 12 square.

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Similarly, if you multiply five, three, four with four, you will get twenty 12 and 16.

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And that is also a Pythagoras intraplate.

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So this is a very useful property.

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You take any by intraplate and you multiply it with the number or you divide it with the number, you

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will get another Pythagorean triplet.