Math, asked by pavangoudar2004, 11 months ago

sum of the area of two squares is 468 m square if the difference between their perimeter is 24 metre find the sides of the two square​

Answers

Answered by hari181818
1

Answer:

Step-by-step explanation:

let the side of smaller square be x

its perimeter be 4*x

perimeter of larger square is 4x +24

side of a larger square =4x+24/4

side of larger square =x+6

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

x^2+x^2+12x+36=468

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

(2x^2+12x-432=0  )/2

x^2+6x-216=0

-216=18*-12

x=-18,+12

small side =12m

larger side =x+6=12+6

=18m

Answered by Anonymous
56

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Sum of the areas of two squares is 468 m²

∵ x² + y² = 468 . ………..(1) .[ ∵ area of square = side²] → The difference of their perimeters is 24 m.

∵ 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),

∵ 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),

∵ y = x – 6

⇒ y = 18 – 6

∴ y = 12 m

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

Hope it's Helpful....:)

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