Tamil Nadu Board Solutions for Chapter: Geometry, Exercise 8: Exercise 4.3

A man goes $18 \mathrm{m}$ due east and then $24 \mathrm{m}$ due north. Find the distance of his current position from the starting point? (Write the answer in $\mathrm{m}$)

There are two paths that one can choose to go from Sarah's house to Jame's house. One way is to take $\mathrm{C}$ street, and the other way requires to take $\mathrm{A}$ street and then $\mathrm{B}$ street. If the direct path along $\mathrm{C}$ street is shorter by $k \mathrm{mile}$, find the value of $k$.

To get from point $\mathrm{A}$ to point $\mathrm{B}$ you must avoid walking through a pond. You must walk $34 \mathrm{m}$ south and $41 \mathrm{m}$ east. To the nearest meter, how many meters would be saved if it were possible to make a way through the pond?(Write the answer in $\mathrm{m}$).

In the rectangle $\mathrm{WXYZ}, \mathrm{XY}+\mathrm{YZ}=17 \mathrm{cm},$and $\mathrm{XZ}+\mathrm{YW}=26 \mathrm{cm}.$ Calculate the length and breadth of the rectangle?

The hypotenuse of a right triangle is $6 \mathrm{m}$ more than twice of the shortest side. If the third side is $2 \mathrm{m}$ less than the hypotenuse, find the sides of the triangle?

$5 \mathrm{m}$ long ladder is placed leaning towards a vertical wall such that it reaches the wall at a point $4 \mathrm{m}$ high. If the foot of the ladder is moved $1.6 \mathrm{m}$ towards the wall, then find the distance by which the top of the ladder would slide upwards on the wall.( Write the answer in $\mathrm{m}$).

The perpendicular $\mathrm{PS}$ on the base $\mathrm{QR}$ of $∆\mathrm{PQR}$ intersects $\mathrm{QR}$ at $\mathrm{S},$ such that $\mathrm{QS}=3 \mathrm{SR}.$ Prove that $2{\mathrm{PQ}}^2=2{\mathrm{PR}}^2+{\mathrm{QR}}^2.$

In the adjacent figure, $\mathrm{ABC}$ is a right-angled triangle with right angle at $\mathrm{B}$ and points $\mathrm{D},$ $\mathrm{E}$ trisect $\mathrm{BC}$. Prove that $8{\mathrm{AE}}^2=3{\mathrm{AC}}^2+5{\mathrm{AD}}^2.$