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

In the given figure $\angle \mathrm{DFE}=90°$, $\mathrm{FG}\perp \mathrm{ED},\text{ If }\mathrm{GD}=8,\mathrm{FG}=12$. Find  $\mathrm{EG}, \mathrm{FD}$ and $\mathrm{EF}$.

Find the diagonal of a rectangle whose length is $35\mathrm{cm}$ and breadth is $12\mathrm{cm}$

In the given figure $,\mathrm{M}$ is the midpoint of $\mathrm{QR}$, $\angle \mathrm{PRQ}=90°$
Prove that, ${\mathrm{PQ}}^2=4{\mathrm{PM}}^2-3{\mathrm{PR}}^2$.

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

In the given figure seg $\mathrm{PS}$ is the median of $\Delta \mathrm{PQR}$ and $\mathrm{PT}\perp \mathrm{QR}$
Prove that, ${\mathrm{PR}}^2={\mathrm{PS}}^2+\mathrm{QR}\times \mathrm{ST}+{\left(\frac{\mathrm{QR}}{2}\right)}^2$

In the given figure seg PS is the median of $\mathrm{\Delta PQR}$ and $\mathrm{PT}\perp \mathrm{QR}$ Prove that,

${\mathrm{PQ}}^2={\mathrm{PS}}^2-\mathrm{QR}\times \mathrm{ST}+{\left(\frac{\mathrm{QR}}{2}\right)}^2$