Let the side of a square is x m.
Perimeter of that square = 4x m
Difference in perimeter is 24 m
Perimeter of second square
= 4x + 24 m
Then, side of second square
= (4x + 24)/4 = 4(x + 6)/4 = (x + 6)m
Area of first square = x2 sq m
Area of second square
= (x + 6)2 sq m = x2 + 12x + 36 sq m
Sum of areas of both squares = 468 sq m
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 + 18)(x – 12) = 0
when x + 18 = 0, then x = -18 (not possible)
or x – 12 = 0, then x = 12
∴ x = 12
Side of smaller square = 12 m
and side of larger square
= x + 6 = 12 + 6
= 18 m
Thus sides of both squares are 12 m. and 18 m respatively