Question

the perimeter of a square exceeds that of another by 24 cm and the area of the larger square is 84 sq cm more than the area of the smaller one.

Answer 1

Step-by-step explanation:

Let S

1

and S

2

be two squares. Let the side of the square S

2

be x cm in length.

Then, the side of square S

1

is (x+4)cm

Area of square S

1

=(x+4)

2

and Area of square S

2

=x

2

It is given that,

(Area of square S

1

)+(Area of square S

2

)=400cm

2

⇒(x+4)

2

+x

2

=400

⇒(x

2

+8x+16)+x=400⇒2x

2

+8x−384=0⇒x

2

+4x−192=0

⇒x

2

+16x−12x−192=0⇒(x+16)(x−12)=0⇒x=12orx=−16

As the length of the side of a square cannot be negative. Therefore, x=12

Side of square S

1

=x+4=12+4=16cm

Side of square S

2

=12cm