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
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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
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Verified answer
Answer:
A' : A = 4 : 1
P' : P = 2 : 1
Step-by-step explanation:
Given :
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
★Solution:-
Hence , A':A = 4:1 and P': P = 2:1.