The hypotenuse of a garden in the shape of a right triangle is $1$ metre more than twice the shortest side. If the longer side containing the right angle is $7$ metres more than the shorter side,find the sides of the garden.

For going to a city $B$ from city $A$,there is a route via city $C$ such that $AC \perp CB$,$AC = 2x \, km$ and $CB = 2(x+7) \, km$. It is proposed to construct a $26 \, km$ highway which directly connects the two cities $A$ and $B$. Find how much distance will be saved in reaching city $B$ from city $A$ after the construction of the highway (in $km$).

If one root of $x^{2}-5x+6=0$ is also the root of $x^{2}+3x+c=0$,then $c = \ldots$

The speed of the flow of a river is $3 \, km/hr$. $A$ motorboat goes $12 \, km$ downstream and comes back in a total time of $3$ hours. Find the speed of the motorboat in still water. (The speed of flow of water is less than the speed of the boat.)

$A$ person,rowing at the rate of $5 \, km/h$ in still water,takes thrice as much time in going $40 \, km$ upstream as in going $40 \, km$ downstream. Find the speed of the stream in $km/h$.

$\square XYZW$ is a rectangle. If $XY + YZ = 17$ and $XZ + YW = 26$,find $XY$ and $YZ$ (given $XY > YZ$).