Question

if the diagonal of a square is increased by 65 % then find the percentage change in area

Answer 1

Answer:

56.25%

Step-by-step explanation :

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

Let the new side be 'a1′.

After increasing the side of square by 25%,

a1 = a + a×25/100

a1 = a(1+1/4)

=> a1 = (5/4)×a

Old Area of the square = a^2

New Area = a1^2 = ((5/4)×a)^2

= (25/16)a^2

Increase in area = New area - Old area

Increase in area = 25/16×a^2 - a^2 = ((25/16) - 1)a^2 = (9/16)a^2

Percentage increase in area =(9/16)×100 = 56.25%