If the side of square P is x and the side of square Q is y, we have x+y=26. In addition, 3*the perimeter of P+8*4y=3*4x+32y=12x+32y=492.
We have
x+y=26
12x+32y=492
Multiplying the first equation by -12 and adding it to the second, we get
20y=180 and dividing by 20 we get y=9. Plugging it into the first equation, we get 26-9=17=x. Since the area of square P is x^2 and Q is y^2,
x^2+y^2=19^2+7^2=410=the sum of the squares