Question

30 Points !!!!!

Find the values of x and y that produce the following Pythagorean triples :
1.) 65, 72, 97
2.) 25, 312, 313
3.) 39, 760, 761

Please show work if you can!

Answer 1

Let
`x` and
`y` be two legs of a right triangle. By Pythagoras' theorem, the hypotenuse will have length
`√(x^2+y^2)`:


`x^2+y^2=(√(x^2+y^2))^2`

What you should do is read the first two values in the given lists as
`x` and
`y`, and the third as
`√(x^2+y^2)`.

So for example, if I gave you the list 3, 4, 5, we take


`x=3`

`y=4`

`\implies√(x^2+y^2)=√(9+16)=√(25)=5`

Since
`√(x^2+y^2)=x^2+y^2`, it follows that (3, 4, 5) is indeed a Pythagorean triple.

Let's check with the first problem: If
`x=65` and
`y=72`, we have


`√(x^2+y^2)=√(9409)=97`

which means (65, 72, 97) is also a Pythagorean triple.