A rod of height $6 cm$ is displaced $90 cm$ from the foot of a mountain of height $126 cm$. Find the distance of the top of the mountain from the vertex of the rod.

One of the sides of a right- angled triangle is $36 cm$ and the sum of the hypotenuse and another side is $54 cm$. Find the length of the hypotenuse and another side. 

The hypotenuse of a right-angled triangle is $26 cm$ and the difference between the other two sides is $14 cm$. Find the length of the two sides.

The perimeter of a right-angled triangle is $60 cm$ and hypotenuse is $26 cm$. Find the lengths of its other two sides.

The perimeter of a right-angled isosceles triangle is $\sqrt{2}\left(\sqrt{2}+1\right) m$. Find the length of the hypotenuse. Also, find the area of the triangle.

The two sides adjacent to the right-angle triangle are $9 cm$ and $12 cm$. Find the length of the perpendicular drawn from the vertex to the hypotenuse.

The perimeter of an equilateral triangle is same as its area. Find its length of side.

The perimeter of the floor of a room is $18 m$. If the height of the room be $3 m$, then its area the four walls is