Question

Sum of the area of two squares is 400 cm². If the difference of their perimeters is 16 cm, find the sides of two squares.

Answer 1

SOLUTION :  

Let the length of each side of a square be x . Then its perimeter = 4x

[Perimeter of a square = 4 × side]

Given : Difference of the perimeters of two squares = 16 m

Perimeter of second square - perimeter of first square = 16

Perimeter of second square - 4x = 16

Perimeter of second square = 16 + 4x

Length of square = perimeter of square/4

Length of each side of second square = (16 + 4x)/4  

= 4(4 + x)/4  

Length of each side of second square = (4 + x) m

Given : Sum of the area of two squares = 400 m²

Area of first square + Area of second square = 400 m²

x² + (4 + x)² = 400

[Area of a square = side²]

x² + (4)² + x² + 2 × 4 × x =  400

[(a+b)² = a² + b² + 2ab]

2x² + 16 + 8x = 400

2x² + 8x + 16 - 400 = 0

2x² + 8x - 384 = 0

2(x² + 4x - 192) = 0

x² + 4x - 192 = 0

x² + 16x - 12x - 192 = 0  

[By middle term splitting]

x(x + 16) - 12 (x + 16) = 0

(x  + 16)(x - 12) = 0

(x  + 16) = 0 or (x - 12) = 0

x = - 16  or x = 12

Since, side can't be negative ,so x ≠ - 16

Therefore, x = 12

Side of first square = (x) = 12 m

Side of second square = 4 + x  

Side of second square = 4 + 12 = 16 m

Side of second square = 16 m

Hence, the side of a square is 12 m and side of second square is 16 m.

HOPE THIS ANSWER WILL HELP YOU .....

Answer 2

Answer:

Length of side of one square is ( 12 + 4 ) or 16 cm and length of side of other square is 12 cm.

Step-by-step explanation:

Let the side of 1st square be a cm and side of 2nd square be b cm,

So,

Area of 1st square = a^2 cm^2

Area of 2nd square = b^2 cm^2

Perimeter of 1st square = 4a cm

Perimeter of 2nd square = 4b cm

According to the question : -

= > Sum of area of two squares = 400 cm^2

= > a^2 + b^2 = 400        ...( i )

Also, given that the difference between the perimeters is 16 cm : -

= > 4a - 4b = 16

= > a - b = 4

= > a = 4 + b

Substituting the value of a in ( i )  :

= > ( 4 + b )^2 + b^2 = 400

= > 16 + b^2 + 8b + b^2 - 400 = 0

= > 2b^2 + 8b - 384 = 0

= > b^2 + 4b - 192 = 0

= > b^2 + ( 16 - 12 )b - 192 = 0

= > b^2 + 16b - 12b - 192 = 0

= > b( b + 16 ) -12( b + 16 ) = 0

= > ( b + 16 ) ( b - 12 ) = 0

= > b =- 16 or 12

Since b is side of a square, it can't be -ve. Therefore b = 12

Hence,

Length of side of one square is ( 12 + 4 ) or 16 cm and length of side of other square is 12 cm.