# Sum of areas of 2 squares is 468m^. If difference of their perimeters is 24m,then find the sides of 2 squares.

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The Brainliest Answer!

Let the side of the smaller square be y.

According to the question, x² + y² = 468 --------- (1)

Perimeters of the squares = 4x and 4y.

⇒ 4x - 4y = 24

⇒ x– y = 6

⇒ x= 6 + y

x² + y² = 468

Substituting the value of x in equation (1)

⇒ (6+y)² + y² = 468

⇒ 2y² + 12y + 36 = 468

⇒ y²+ 6y + 18 = 234

⇒ y² + 6y - 216 = 0

⇒ (y – 12)(y + 18) = 0

⇒ y = 12 or -18

Since y denotes a length, it cannot be negative.

∴ y = 12

⇒ x = (12 + 6) = 18 m

∴ Sides of the squares are 18 m and 12 m.