The perimeter of a triangle is $50\mathrm{cm}$. One side of the triangle is $4\mathrm{cm}$ longer than the smallest side and the third side is $6\mathrm{cm}$ less than twice the smallest side. If the area of the triangle is $a\sqrt{30} c{m}^2$. Find the value of $a$.

The triangular side walls of a flyover have been used for advertisements. The sides of the walls are $13 \mathrm{m}, 14 \mathrm{m}, 15 \mathrm{m}$. The advertisements yield an earning of $₹2000$ per ${\mathrm{m}}^2$ a year. A company hired one of its walls for $6$ months. If the company paid $₹k$, then find the value of $k$.

The perimeter of an isosceles triangle is $42 \mathrm{cm}$ and its base is $1\frac{1}{2}$ times of each of the equal sides. If length of the longest side of the triangle is $k \mathrm{cm}$, then find the value of $k$.

The perimeter of an isosceles triangle is $42 \mathrm{cm}$ and its base is $1\frac{1}{2}$ times, each of the equal sides. If the area of the triangle is $k c{m}^2$. Then find the value of $k$.

The perimeter of an isosceles triangle is $42 \mathrm{cm}$ and its base is $1\frac{1}{2}$ times, each of the equal sides. Find the height of the triangle.

The area of an equilateral triangle is $36\sqrt{3} {\mathrm{cm}}^2$. If its perimeter is $k \mathrm{cm}$, then find the value of $k$.

If the area of the equilateral triangle is $81\sqrt{3} {\mathrm{cm}}^2$ and  its height is $K\sqrt{3} cm$. Find the value of $K$

Each side of an equilateral triangle measures $8\mathrm{cm}$. If the area of the triangle is $k c{m}^2$, Find the value of $k$ correct to $2$ places of decimal. (Take $\sqrt{3}=1.732$).

Each side of an equilateral triangle measures $8 \mathrm{cm}$.If the height of the triangle, correct to $2$ places of decimal is $h \mathrm{cm}$, find the value of $h$. [Take$\sqrt{3}=1.732$]