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
Answers
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:
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