Question

Tess created a Pythagorean triple of (24, 32, 40) by multiplying the known Pythagorean triple 3, 4, and 5 by 8. Is Tess correct? Can a Pythagorean triple be created using multiples of a known Pythagorean triple.
Yes, as long as each number in the Pythagorean triple is multiplied by the same whole number.
Yes, as long as each number in the Pythagorean triple is multiplied by a different whole number.
No, Pythagorean triples only exist with small numbers.
No, multiplying a known Pythagorean triple by a whole number will not create a Pythagorean triple.

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Answer 1

Answer:

Yes.

To go in depth, the pythagorean theorem is a^2+b^2=c^2. C is always the longest side, or hypotenuse, so you would replace c with 40. A and B can be in any order, so let's replace a with 24 and b with 32.

A Squared=24 Squared=576

B Squared=32 Squared=1024

C Squared=40 Squared=1600

Now to test it:

576+1024=1600

1600=1600

So yes, it is a pythagorean triple.

* * * * *

There is a simpler method.

3-4-5 is a well known Pythagorean triple. Therefore, any multiple of the triple is also a Pythagorean triple.

24-32-40 are 8 times the corresponding numbers and so they form a Pythagorean triple.

Answer 2

Answer:

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