Question

a) The area and the perimeter of a square are A and P respectively. If the sides are doubled, the area becomes A' and the perimeter, P'. Find (i) A': A, and (ii) P':P.​

Answer 1

Step-by-step explanation:

Let the side of the square be x

Perimeter,P= 4x

Area A = x^2

When sides are doubled, length of side = 2x

P'= 8x

A' = 4x^2

A' = 4x^2/x^2 = 4:1

P" :P = 8x/4x = 2:1

Answer 2

Answer :

• A' : A = 4 : 1
• P' : P = 2 : 1

Step-by-step explanation :

Given :

• The area and the perimeter of a square are A and P respectively.
• If the sides are doubled, the area becomes A' and the perimeter, P'

To find :

(i) A' : A

(ii) P' : P

Formulae :

Area of square = (side)²

Perimeter of square = 4(side)

Solution :

Let "a" be the side of the square.

​

➟ Area of the square = (side)²

 A = (a)²

 A = a²

➟ Perimeter of the square = 4(side)

 P = 4(a)

 P = 4a

Now, the sides are doubled.

So, new side of the square, a' = 2a

➟ Area of the square = (side)²

 A' = (a')²

 A' = (2a)²

 A' = 4a²

➟ Perimeter of the square = 4(side)

 P' = 4(a')

 P' = 4(2a)

 P' = 8a

Finding the ratio ;

(i) A' : A = 4a² : a²

    A' : A = 4 : 1

(ii) P' : P = 8a : 4a

    P' : P = 2 : 1