The perimeter of a triangle is $30 \text{ cm}$ and its area is $30 \text{ cm}^2$. If the largest side measures $13 \text{ cm}$,then what is the length of the smallest side of the triangle? (in $\text{cm}$)

The sum of all interior angles of a regular polygon is twice the sum of all its exterior angles. The number of sides of the polygon is

The area of the incircle of an equilateral triangle of side $42 \ cm$ is (in $cm^2$)

$A$ room $5\, m \times 8\, m$ is to be carpeted leaving a margin of $10\, cm$ from each wall. If the cost of the carpet is ₹ $18$ per $m^2$,then the cost of carpeting the room will be (in $Rs.$)

$A$ playground is in the shape of a rectangle. $A$ sum of ₹ $1,000$ was spent to make the ground usable at the rate of $25$ $paisa$ per $m^2$. The breadth of the ground is $50\, m$. If the length of the ground is increased by $20\, m$,what will be the expenditure in rupees at the same rate per $m^2$?

The ratio of the corresponding sides of two similar triangles is $3:4$. The ratio of their areas is