Question

Find the Pythagorean Triples using the values, $m=4$ and $n=8$.

Answer 1

Condition for constructing Pythagorean triples:
When $m$ and $n$ are any two positive integers $(m<n)$:

$a=n^2-m^2$

$b=2nm$

$c=n^2+m^2$

Then $a,b$ and $c$ are Pythagorean triple

Here $m=4$ and $n=8$

$\therefore 8^2-4^2$

$\Rightarrow 64-16=48$

$\therefore b=2\times 8\times 4=64$

$\therefore c=8^2+4^2$

$\Rightarrow 64+16=80$

Hence, Pythagorean triples are $48,64,80$.