Let the side of larger square = x m
let the side of smaller square = y m
According to question, x² + y² = 468 …(i)
Difference between parimeters, 4x – 4y = 24
⇒ x – y = 6
⇒ x = 6 + y …(ii)
Putting the value of x in equation (i), we get
(y + 6)² + y² = 468
⇒ y² + 12y + 36 + y² = 468
⇒ 2y² + 12y – 432 = 0
⇒ y² + 6y – 216 = 0
⇒ y² + 18y – 12y – 216 = 0
⇒ y(y + 18) – 12(y + 18) = 0
⇒ (y + 18) (y – 12) = 0
⇒ (y + 18) = 0 or (y – 12) = 0
Either y = – 18 or y = 12
But, y ≠ – 18, as x is the side of square, which can’t be negative. So, y = 12
Hence, the side of smaller square = 12 m
Putting the value of y in equation (ii). we get
side of large square = x = y + 6 = 12 + 6 = 18 m.