Hi, 



p^2 + (p+5)^2 = 625 cm^2

2p^2 + 10 p + 25 = 625cm^2

2P^2 + 10 p - 600cm^2 = 0

p^2 + 5p - 300cm^2 = 0

factoring

(p + 20)(x - 15) = 0

(p + 20)=0

p = -20 cannot use this solution

(x - 15) = 0

x = 15cm

15cm and 20cm are the sides of the squares 

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