Math, asked by BrainlyHelper, 1 year ago

Sum of the areas of two squares is 640 m². If the difference of their perimeters is 64 m. Find the sides of the two squares.

Answers

Answered by nikitasingh79
26

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

Answered by Anonymous
34

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\sf\huge{\bold{\underline{Question}}}!

▶Sum of the areas of two squares is 640 m². If the difference of their perimeters is 64 m. Find the sides of the two squares..

Solution=>

let the sides of the two squares be 'x' and 'y'

according to the question!

sum of areas = 640m^{2}

i.e,

x^{2}+y^{2} = 640m^{2}==(1)

and

Difference of perimeter = 64m

i.e,

4x -4y = 64

4(x-y)=64

x - y = 16

x = 16 +y ==(2)

from equation (1)

x^{2}+y^{2} = 640m^{2}

(16+y)^{2}+y^{2} = 640m^{2}

256+2y^{2}+32y = 640

2y^{2}+32y = 384

2y(y+16) = 384

y^{2}+16y= 192

y^{2}+16y-192= 0

factorising..

y^{2}+24y-8y-192=0

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

1. y + 24 = 0

y = -24.(sides can't be negative)

2. y-8=0

y = 8

x= y +16

x = 24


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