Question

the area and perimeter of a square are A and P respectively if the sides are doubled the area become A' the and the perimeter become P'Find (i)A':A and (ii)P':P​

Answer 1

Answer:

A' : A = 4 : 1

P' : P = 2 : 1

Step-by-step explanation:

Given :

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

To find :

A' : A and P' : P

Solution :

Let 'a' be the length of the side of the square.

Area of the square, A = (side)² = a²

Perimeter of the square, P = 4(side) = 4a

The sides are doubled :

new side, a' = 2a

➟ New area of the square = (new side)²

A' = (a')²

A' = (2a)²

A' = 4a²

➟ New Perimeter of the square = 4(new 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

Answer 2

★Solution:-

• We Have side of square = a

• Area of Square = (side)² = a²

• Perimeter Of Square = 4× side =4a

• If side is doubled = 2a

• Area of new Square = (2a²) =4a²

• Perimeter Of New Square = 4×2a = 8a

• Ratio Of Area ,

• $(i) = \frac{a {}^{1} }{a} = \frac{4a {}^{2} }{ {a}^{2} } = \frac{4}{ 1} \\ =4 :1$

• Ratio Of Perimeters,

• $(ii) \frac{p {}^{1} }{p} = \frac{8a}{4a} = \frac{2}{1} \\ =2 :1$

Hence , A':A = 4:1 and P': P = 2:1.