Answer :

Given:

Side(**a**) of square **ABCD** = **5**cm.

Perimeter(**P _{2}**) of square

**PQRS**=

**40**cm.

We know that Perimeter of a square having side length ‘**x**’ is ‘**4x**’.

We also know that Area of a square having side length ‘**x**’ is ‘**x ^{2}**’.

So perimeter(**P _{1}**) of square

**ABCD**is

**4a**

i.e, **P _{1}** =

**4a**

⇒ P_{1} = 4 × 5

⇒ **P _{1} = 20**cm.

Area(**A _{1}**) of square

**ABCD**is

**a**

^{2}i.e, **A _{1}** =

**a**

^{2}⇒ A_{1} = 5^{2}

⇒ **A _{1}** = 25cm

^{2}.

Let's find the side length(b) of square **PQRS**

We have **P _{2}** =

**4b**

⇒ 4b = 40

⇒ b =

⇒ **b** = **10**cm.

Area(**A _{2}**) of square

**PQRS**is

**b**

^{2}i.e, **A _{2}** =

**b**

^{2}⇒ A_{2} = 10^{2}

⇒ **A _{2}** =

**100**cm

^{2}.

Let's find the ratio of Perimeters(**RP**) of both squares

i.e, **r _{p}** =

**⇒** r_{p} =

⇒ **r _{p} =**

Let's find the ratio of Areas(**r _{A}**) of both squares

i.e., **r _{ag}** =

⇒ r_{ag} =

⇒ **r _{ag} =**

The ratio of perimeters is.

The ratio of area is.

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