Maharashtra Board Solutions for Chapter: Pythagoras Theorem, Exercise 2: Practice set 2.2

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 $\mathrm{\Delta ABC},\mathrm{AB}=10,\mathrm{AC}=7,\mathrm{BC}=9$ then find the length of the median drawn from point $C$ to side $A B$

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,

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

In $\mathrm{\Delta ABC}$, point $\mathrm{M}$ is the midpoint of side $\mathrm{BC}$. If ${\mathrm{AB}}^2+{\mathrm{AC}}^2=290{\mathrm{cm}}^2$, $\mathrm{AM}=8\mathrm{cm},$  find $\mathrm{BC}.$

In the given figure point $\mathrm{T}$  is in the interior of rectangle $\mathrm{PQRS}$. Prove that, ${\mathrm{TS}}^2+{\mathrm{TQ}}^2={\mathrm{TP}}^2+{\mathrm{TR}}^2$

(As shown in the figure, draw

Seg $\mathrm{AB}\Vert$ Side $SR$ and  $A-T-B$)