The ratio of the sides of a triangle is $3:4:5$ and its area is $7776 sq.cm$. Find the length of the sides of the triangle and also find the perpendicular distance of its greatest side from the opposite vertex of it.

The length of the base of a right-angled triangle is $5 m$ more than $\frac{1}{2}$ part of its perpendicular drawn on it and the length of the hypotenuse is $9 m$ more than $\frac{4}{5}$ part of its perpendicular. Find the length of the perpendicular. Also, find the area of the triangle.

Perpendicular are drawn from an internal point of an equilateral triangle to its sides. If the lengths of the perpendiculars be $9 cm, 11 cm$ and $10 cm$, then find the sides and area of the triangle.

The length of the medians of a triangle are $9 cm, 12 cm$ and $15 cm$. Find its area.

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.