Question

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.

Answer 1

Answer:

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

$2m,m^2-1,m^2+1$

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

$2m=16$

$\Rightarrow m=8$

Now, $m^2-1=16$

$m^2=17$ will not give integer.

And now, $m^2+1=16$

$m^2=15$  will not get integer value

Hence, the value of m will be 8

And substituting the value in the triplet formula we get

$2m=2\cdot 8=16$ which is given.

$m^2-1=64-1=63$ the other leg and is odd.

And $m^2+1=64+1=65$ the hypotenuse or the longest side.

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

Pythagoras theorem is:

$\text{one side}^2+\text{other side}^2=hypotenuse^2$

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