Find the length of the shortest side

$c^2=a^2+b^2$

$2c^2=2450$

$c=35$

$a+b+c=84$

$a+b+35=84$

$a+b=49$

$a=49-b$

$c^2=a^2+b^2$

$35^2=(49-b)^2+b^2$

$1225=2401-98b+b^2+b^2$

$0=1176-98b+2b^2$

$0=588-49b+b^2$

$b=21$ or $b=28$

So $b$ is either $21$ or $28$ , and $a$ accordingly is either $21$ or $28$ . Therefore the shortest side is $21$ .