Question

The length of the side of a square is decreased by 88%. Find the percentage decrease in the area of the square.​

Answer 1

Step-by-step explanation:

Let the side of square be a.

Length of diagonal is

a

2

+a

2

=a

2

When the length of diagonal is decreased by 15%, current length of diagonal be d

′

=(1−15/100)∗a

2

=0.85∗a

2

Let the side of new square be a

′

Relation between a

′

and d

′

is

d

′

=a

′

2

d

′

=a

′

2

⇒0.85∗a

2

=a

′

2

⇒a

′

=0.85a

Area of new square is (a

′

)

2

=(0.85a)

2

=0.7225a

2

Percent decrease in area is

a

2

a

2

−0.7225a

2

∗100=27.75%