Question

If the area of a square reduce by 51%, the percentage reduction in its perimeter will be:

49%
70%
30%
51%

PLEASE TELL THE ANSWER AND GIVE EXPLANATION

Answer 1

Step-by-step explanation:

49

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Answer 2

Given : The area of a square reduced by 51%

To find : The percentage reduction in its perimeter.

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the percentage reduction in perimeter)

Let, one side of the square = a

Initial perimeter of the square = 4 × side = 4a

Initial area of the square = (side)² = a²

After getting reduced by 51% the area of the square becomes :

= a² - (a² × 51%)

= a² - (51a²/100)

= (100a²-51a²)/100

= 49a²/100

So, the new length of one side of the square :

= √(Area of the square after getting reduced by 51%)

= √(49a²/100)

= 7a/10

New perimeter :

= 4 × new length of one side of the square

= 4 × (7a/10)

= 14a/5

Reduction in perimeter is :

= Initial perimeter - New perimeter

= 4a - (14a/5)

= (20a-14a)/5

= 6a/5

Percentage reduction in perimeter :

= 100 × (Reduction in perimeter ÷ Initial perimeter)

= 100 × [(6a/5) ÷ 4a]

= 100 × [(6a/5) × (1/4a)]

= 100 × (3/10)

= 30%

(This will be considered as the final result.)

Hence, if the area of a square reduce by 51%, the percentage reduction in its perimeter will be 30%