$A$ train travels $360\, km$ at a uniform speed. If the speed had been $5\, km/h$ more,it would have taken $1\, hour$ less for the same journey. Find the speed of the train (in $km/h$).

Find two numbers whose sum is $27$ and product is $182$.

The diagonal of a rectangular field is $60\, m$ more than the shorter side. If the longer side is $30\, m$ more than the shorter side,find the sides of the field. (in $m$)

Find the values of $k$ for the following quadratic equation,so that it has two equal roots:
$2 x^{2}+k x+3=0$

Check whether the following is a quadratic equation:
$x(x+1)+8=(x+2)(x-2)$

$A$ rectangular park is to be designed whose breadth is $3\, m$ less than its length. Its area is to be $4\, m^2$ more than the area of a park that has already been made in the shape of an isosceles triangle with its base as the breadth of the rectangular park and of altitude $12\, m$ (see Figure). Find its length and breadth.