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

Therefore, their perimeter will be 4x and 4y respectively

And area of the squares will be x^{2} and y^{2} respectively.

Given,

4x – 4y = 24

x – y = 6

x = y + 6

Also, x^{2 }+^{ }y^{2} = 468

⇒ (6 + y^{2}) + y^{2} = 468

⇒ 36 + y^{2} + 12y + y^{2} = 468

⇒ 2y^{2} + 12y + 432 = 0

⇒ y^{2} + 6y – 216 = 0

⇒ y^{2} + 18y – 12y – 216 = 0

⇒ y(y +18) -12(y + 18) = 0

⇒ (y + 18)(y – 12) = 0

⇒ y = -18, 12

As we know, the side of a square cannot be negative.

Hence, the sides of the squares are 12 m and (12 + 6) m = 18 m.

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