Answer:

Let the side of the first square = x m say

Then perimeter of the first square = 4x

[∵ p=4.side]

By problem, perimeter of the second square = 4x + 24 (or) 4x -24

Now sum of the areas of the two squares is given as 468 m²

x² (x + 6)² =

x² + x² + 12x + 36 =

2x² + 12x + 36 - = 0

2x² + 12x - = 0

x² + 6x - = 0

x² + 18x - x - = 0

x(x + 18) - (x + 18) = 0

(x + 18)(x - ) = 0

x + 18 = 0 (or) x - = 0

x = -18 (or)

But x can't be negative.

∴ x =

i.e., side of the first square =

∴Perimeter = 4 × =

∴ Perimeter of the second square + 24 =