Math, asked by pramobtiwari, 11 months ago

plzzz solve in copy , Sum of the areas of 2 squares is 468 sqm,if the difference between their perimeters is 24m.find the sides of the square ♥️​

Answers

Answered by Anonymous
2

let sides of squares be a and b

Sum of areas = 468

a^2 + b^2 = 468

Difference between perimeters = 24

4( a-b)= 24 , a>b

a- b= 24/4 = 6

a= 6 + b

( 6+ b)^2 + b^2 = 468

36 + b^2 + 12b + b^2 -468= 0

2b^2 + 12b - 432 = 0

b^2 + 6b - 216= 0

b^2 +18 b- 12b -216= 0

b( b+18) -12( b+18)= 0

b-12)(b+18)= 0

b= 12,-18

neglect -18

So b= 12

a= 6+b= 6+12= 18


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Answered by Anonymous
0

Step-by-step explanation:

Answer:

→ 18m and 12 m .

Step-by-step explanation:

Let the sides of two squares be x m and y m respectively .

Case 1 .

→ Sum of the areas of two squares is 468 m² .

A/Q,

∵ x² + y² = 468 . ...........(1) .

[ ∵ area of square = side² . ]

Case 2 .

→ The difference of their perimeters is 24 m .

A/Q,

∵ 4x - 4y = 24 .

[ ∵ Perimeter of square = 4 × side . ]

⇒ 4( x - y ) = 24 .

⇒ x - y = 24/4.

⇒ x - y = 6 .

∴ y = x - 6 ..........(2) .

From equation (1) and (2) , we get

∵ x² + ( x - 6 )² = 468 .

⇒ x² + x² - 12x + 36 = 468 .

⇒ 2x² - 12x + 36 - 468 = 0 .

⇒ 2x² - 12x - 432 = 0 .

⇒ 2( x² - 6x - 216 ) = 0 .

⇒ x² - 6x - 216 = 0 .

⇒ x² - 18x + 12x - 216 = 0 .

⇒ x( x - 18 ) + 12( x - 18 ) = 0 .

⇒ ( x + 12 ) ( x - 18 ) = 0 .

⇒ x + 12 = 0 and x - 18 = 0 .

⇒ x = - 12m [ rejected ] . and x = 18m .

∴ x = 18 m .

Put the value of 'x' in equation (2), we get

∵ y = x - 6 .

⇒ y = 18 - 6 .

∴ y = 12 m .

Hence, sides of two squares are 18m and 12m respectively .

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