Question

If each side of a square is increased by 25%, find the percentage change in its area?

A) 65.25 B) 56.25 C) 65 D) 56

Answer 1

Given :

• Each side of a square is increased by 25%

To find :

• The percentage change in its area =?

Step-by-step explanation :

We know that,

Area of square = a²

So, New side of square = a + (25/4) = 5a/4.

Now,

New area of square = (New side of square)²

Substituting the values, we get,

= (5a/4)²

= (25/16)a²

Percentage change in Area,

= [{(25/16)a² - a²}/a²] × 100

= [{(9/16)a²}/a²] × 100

= 225/4

= 56.25

Therefore, the percentage change in its area = 56.25 %.

Hence, Option, B) 56.25 ✔️

Answer 2

Answer:

Correct option: B) 56.25

Given :

► Each side of a square is increased by 25%

To find :

The percentage change in its area.

Solution:

We are given,

► Each side of a square is increased by 25%.

We know that,

Area of square = p².

But According to given condition.

The area increased by 25%.

The new area is :

⛬ New side of square = p + (25/4) = 5p/4.

Now,

➨ New area of square = (New side of square)²

➨ New area of square = ( 5p / 4 )²

➨ New area of square = ( 25 / 16 )p²

Now, Percentage change in Area,

⇛ [ {(25/16)p² - p² }/p²] × 100

⇛ [{(9/16)p²} / p²] × 100

⇛ 225/4

⇛ 56.25

Hence , the percentage change in its area =

56.25 %.

correct option is: B) 56.25