The area of an equilateral triangle is $81\sqrt{3} {\mathrm{cm}}^2$. Its height is

The base of a triangular field is three times its altitude. If the cost of sowing the field at $₹58$ per hectareis $₹783$, find its base and height.

There is a triangle whose sides are $18 \mathrm{cm}, 24 \mathrm{cm}$ and $30 \mathrm{cm}$ in length. If the length of the altitude corresponding to the smallest side is $k \mathrm{cm}$, then find the value of $k$.

The triangular field's sides are $91 \mathrm{m}, 98 \mathrm{m}$, and $105 \mathrm{m}$ in length. If the height corresponding to the longest side is $\mathrm{k} \mathrm{m}$ then, write the value of $\mathrm{k}$ as a final answer in the form of decimal.

The sides of triangle are in the ratio $5:12:13$ and its perimeter is $150 \mathrm{m}$. If the area of triangle is $k {\mathrm{m}}^2$, then find the value of $k$.

The perimeter of a triangular field is $540 \mathrm{m}$ and its sides are in the ratio $25:17:12$. If the cost of ploughing the field at $₹5\text{ per }{\mathrm{m}}^2$ is $₹x$, then find the value of $x$.

Two sides of a triangular field are $85 \mathrm{m}$ and $154 \mathrm{m}$ in length and its perimeter is $324 \mathrm{m}$. If the area of the field is $k {\mathrm{m}}^2$ then find $k$.