Let

x = the side of the first square, x>0

4x = the perimeter of the first square

x^2 = the area of the first square

y = the side of the second square, y>0

4y = the perimeter of the second square

y^2 = the area of the second square

4x - 4y = 24 divide both sides by 4

x - y = 6

y = x - 6

And we also know that:

x^2 + y^2 = 468

Plug y = x - 6 into the above equation:

x^2 + (x - 6)^2 = 468

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click here to see the equation solved for x

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x = 18 cm

y = 18 - 6

y = 12 cm

The sides of the two squares are: the first square's side is 18 cm while the second square's side is 12 cm.