The perimeter of a triangular field is $420\, m$ and its sides are in the ratio $6: 7: 8$. Find the area of the triangular field (in $m^2$).

$A$ floral design on a floor is made up of $16$ tiles which are triangular,the sides of the triangle being $9\, cm, 28\, cm$ and $35\, cm$ (see Fig.). Find the cost of polishing the tiles at the rate of $50p$ per $cm^2$.

The sides of a triangle are $35 \text{ cm}$,$54 \text{ cm}$,and $61 \text{ cm}$,respectively. The length of its longest altitude is:

The sides of a triangular field are $41\, m$,$40\, m$,and $9\, m$. Find the number of rose beds that can be prepared in the field,if each rose bed,on an average,needs $900\, cm^2$ space.

The perimeter of an isosceles triangle is $32 \, cm$. The ratio of the equal side to its base is $3:2$. Find the area of the triangle.

Write True or False and justify your answer.
The area of the isosceles triangle is $\frac{5}{4} \sqrt{11} \, cm^2$,if the perimeter is $11 \, cm$ and the base is $5 \, cm$.