Maharashtra Board Solutions for Chapter: Pythagoras Theorem, Exercise 1: Practice set 2.1

In the given figure $\angle \mathrm{QPR}=90°$. Seg $\mathrm{PM}\perp seg\mathrm{QR}$ and $\mathrm{Q}-\mathrm{M}-\mathrm{R}$, $\mathrm{PM}=10,\mathrm{QM}=8,\text{ find }\mathrm{QR}$.

 Find $\mathrm{RP}$  and $\mathrm{PS}$ using the information given in$∆PSR .$

For finding $\mathrm{AB}$ and $BC$ with the help of information given in figure complete following activity. 

$\mathrm{AB}=\mathrm{BC}\dots \dots \dots$

$\therefore \angle \mathrm{BAC}=......$

$\therefore AB=BC=....\times AC$

$=....\times \sqrt{8}$

$=....\times 2\sqrt{2}$

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, ${\mathrm{PQ}}^2=4{\mathrm{PM}}^2-3{\mathrm{PR}}^2$.

Walls of two buildings on either side of a street are parallel to each other. A ladder $5.8\mathrm{m}$ long is placed on the street such that its top just reaches the window of a building at the height of $4\mathrm{m}$ . On turning the ladder over to the other side of the street, its top touches the window of the other building at a height $4.2\mathrm{m}$. Find the width of the street.