Question

the sum of area of two squares is 640 if the difference in their perimeter be 64 m then find sides of two sq

Answer 1

Hi,

Here's ur answer:-

Let the side of one square be x and the other square's side be y

Area of first square = x²

Area of second square = y²

According to question,

x²+y²= 640

Perimeter of 1st square = 4x

Perimeter of 2nd square = 4y

So,

4x-4y = 64

=> 4(x-y) = 16×4

=> x-y = 16

So,

We can use formula (x-y)² = x²+y²-2xy

=> (16)² = 640 - 2xy

=> 256 = 640-2xy

=> 2xy = 640-256 = 384

We have found 2xy ,

Now ,we can use formula (x+y)²= x²+y²+2xy

=> (x+y)² = 640+384 = 1024

=> x+y = √(1024) = 32

So,

We can use simultaneous linear equation now.

x+y = 32
x-y = 16
______

2y = 16

=> y = 8

x+y = 32

=> x + 8 = 32

=> x = 32-8 = 14

So, the sides of two squares is 14 cm and 8 cm respectively.

HOPE IT HELPS (^_^)

PLEASE MARK BRAINLIEST

Answer 2

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 = 64 m

Perimeter of second square - perimeter of first square = 64

Perimeter of second square - 4x = 64

Perimeter of second square = 64 + 4x

Length of square = perimeter of square/4

Length of each side of second square = (64 + 4x)/4  

= 4(16 + x)/4  

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

Given : Sum of the area of two squares = 640 m²

Area of first square + Area of second square = 640 m²

x² + (16 + x)² = 640  

[Area of a square = side²]

x² + (16)² + x² + 2 ×16× x =  640

[(a+b)² = a² + b² + 2ab]

2x² + 256 + 32x = 640

2x² + 32x + 256 - 640 = 0

2x² + 32x - 384 = 0

2(x² + 16x - 192) = 0

x² + 16x - 192 = 0

x² + 24x - 8x - 192 = 0  

[By middle term splitting]

x(x + 24) - 8 (x + 24) = 0

(x  + 24)(x - 8) = 0

(x  + 24) = 0 or (x - 8) = 0

x = - 24  or x = 8

Since, side can't be negative ,so x ≠ - 24

Therefore, x = 8

Side of first square = (x) = 8 m

Side of second square = 16 + x  

Side of second square = 16 + 8 = 24 m

Side of second square = 24 m

Hence, the side of a square is 8 m and side of second square is 24 m.

HOPE THIS ANSWER WILL HELP YOU