The side of a square ABCD is 5cm and another square PQRS has perimeter equal to 40cm. Find the ratio of the perimeter of ABCD to perimeter of PQRS. Find the ratio of the area ABCD to the area of PQRS.

Given:

Side(a) of square ABCD = 5cm.

Perimeter(P₂) of square PQRS = 40cm.

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 ‘x²’.

So perimeter(P₁) of square ABCD is 4a

i.e, P₁ = 4a

⇒ P₁ = 4 × 5

⇒ P₁ = 20cm.

Area(A₁) of square ABCD is a²

i.e, A₁ = a²

⇒ A₁ = 5²

⇒ A₁ = 25cm².

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

We have P₂ = 4b

⇒ 4b = 40

⇒ b =

⇒ b = 10cm.

Area(A₂) of square PQRS is b²

i.e, A₂ = b²

⇒ A₂ = 10²

⇒ A₂ = 100cm².

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.