The sides of a triangle are $a \, cm$,$b \, cm$,and $c \, cm$. Also,its semi-perimeter is $s \, cm$. If $s - a = 10 \, cm$,$s - b = 15 \, cm$,and $s - c = 12 \, cm$,then $s = \dots \, cm$.

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 cost of levelling the ground in the form of a triangle having the sides $51 \, m$,$37 \, m$,and $20 \, m$ at the rate of $Rs \, 3$ per $m^2$ is $Rs \, 918$.

Sides of a triangle are in the ratio of $12 : 17 : 25$ and its perimeter is $540 \, cm$. Find its area.

Write True or False and justify your answer.
In a triangle,the sides are given as $11 \, cm$,$12 \, cm$,and $13 \, cm$. The length of the altitude corresponding to the side of length $12 \, cm$ is $10.25 \, cm$.

The perimeter of a triangle is $50 \, cm$. One side of a triangle is $4 \, cm$ longer than the smaller side and the third side is $6 \, cm$ less than twice the smaller side. Find the area of the triangle.