Pythagorean triples are given by the formula x^2-y^2, 2xy, and x^2+y^2. use the formulas for the pythagorean triples to find a right triangle with leg lengths of 16 and an odd number. show all of your work for full credit.

Let the unknown length be x

We have a formula to find the triplet of a right angle triangle

Put the given length equal to all three terms in the triplet

put 16 equal to all above three but number comes out has to be integer.

Now,

will not give integer.

And now,

 will not get integer value

Hence, the value of m will be 8

And substituting the value in the triplet formula we get

which is given.

the other leg and is odd.

And the hypotenuse or the longest side.

Hence, 16,63 and 65 will form a right triangle

Pythagoras theorem is:

Here, 16 and 63 are sides or legs and 65 is the hypotenuse.

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