Final answer:
The dimensions of the square are 12 cm by 12 cm.
Step-by-step explanation:
Let's call the side of the first square x cm and the side of the second square (x - 3) cm. The formula for the area of a square is A = s^2, where s is the length of a side. The sum of the areas of the two squares is given as 225 sq. cm, so we can write the equation:
x^2 + (x - 3)^2 = 225
Simplifying the equation, we get:
2x^2 - 6x + 9 = 225
2x^2 - 6x - 216 = 0
Factoring the equation, we have:
(2x + 18)(x - 12) = 0
Solving for x, we find that x = 12. Therefore, the dimensions of the square are 12 cm by 12 cm.
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