Find the side and perimeter of a square whose diagonal is $10\mathrm{cm}$

Identify, with reason, the given numbers is Pythagorean triplets or not.

$(3,5,4)$

Identify, with reason, the given numbers is Pythagorean triplets or not.

$\left(4, 9, 12\right)$

Identify, with reason, the given numbers are Pythagorean triplets or not

$\left(5, 12, 13\right)$

Identify, with reason, the given numbers are Pythagorean triplets or not

$\left(24, 70, 74\right)$

Identify, with reason, the given numbers are Pythagorean triplets or not

$(10,24,27)$

In $△\mathrm{PQR}$, point $\mathrm{S}$ is the midpoint of side $\mathrm{QR}$. If $\mathrm{PQ}=11,\mathrm{PR}=17,\mathrm{PS}=13$, find $\mathrm{QR}$