The ratio of two sides of a parallelogram is $3:4$. If its perimeter is $56 \mathrm{cm}$, find the lengths of the sides of parallelogram.

The circumference of the base of a cylindrical vessel is $132 cm$ and its height is $25 cm$. Find the radius of the cylinder.

In the figure, $a, b, c$ are the sides of a right triangle where $c$ is the hypotenuse. Prove that the radius $r$ of the circle which touches the sides of the triangle is given by $r=\frac{a+b+c}{2}$.

‘O’ is the centre of the circle. The area of the shaded region in the given figure is $126 c{m}^2 , \overline{PQ} = \overline{PR}$ then the diameter $QR$ is:

In the given figure, three circles with centres $A, B, C$ respectively touch each other externally. If $AB=5cm, BC=7cm$ and $CA=6cm$, then the radius of the circle with centre $A$ is

From the figure of $\odot \left(O,r\right)$ match the following. The correct option is _____

Match

$\left(1\right) \overline{AC}\cup \stackrel{⏜}{ABC}$                 $\left(a\right)2r$

$\left(2\right)\overline{OA}$ length                      $\left(b\right)r$

$\left(3\right)\overline{AC}$ length                      $\left(c\right)\mathrm{\pi r}+2\mathrm{r}$

If the ratio between the length and perimeter of a rectangular plot is $1:3$, then the ratio between the length and breadth of the plot is _____

The sum of the lengths of the sides of a triangle is called its _____

If the perimeter of a square tablecloth is $144 \text{m}$, then one side of the tablecloth will be _____.