In a $∆ABC$, the measure of $BC$ is $y \mathrm{cm}$. If $AB$ is two times $BC$ and $AC$ is $1 \mathrm{cm}$ less than $AB$, then what will be its perimeter?

The first three stages of a sequence are shown below. What is the perimeter of the tenth figure in the sequence?

Pair of identical rectangular strips, each measuring $3$ by $1$, are overlapped in a number of different ways to form three different shapes, shown in the diagram below. Which shape has greatest perimeter?

A man has four sons who are all gardeners. How can he divide his garden as shown at right, into four equal plots of identical size and shape?

The perimeter of a rectangle is $36 \mathrm{cm}.$ What will be length and breadth (in natural numbers) of that rectangle whose area is maximum?

The perimeter of a rectangle is $36 \mathrm{cm}.$ What will be length and breadth (in natural numbers) of that rectangle whose area is minimum?