Final answer:
To solve the problem, set up a system of equations using the formulas for the areas of squares. Find the side lengths of the two squares by solving the equations.
Step-by-step explanation:
To solve this problem, we can set up a system of equations. Let's assume that the side lengths of the two squares are 'x' and 'y'. The area of a square is given by the formula A = side^2. So, the sum of their areas is x^2 + y^2 = 3060 cm² and their difference is x^2 - y^2 = 468 cm².
By rearranging the second equation, we can express x^2 in terms of y^2: x^2 = y^2 + 468.
Substituting this into the first equation, we have y^2 + 468 + y^2 = 3060. Simplifying, we get 2y^2 + 468 = 3060. Solving for y^2, we find y^2 = 1296. Taking the square root of both sides, we get y = 36 cm.
Now, substituting this value of y into the second equation, we can find the value of x. x^2 = y^2 + 468 = 36^2 + 468 = 216 + 468 = 684. Taking the square root of 684, we get x ≈ 26.2 cm.
Therefore, the side lengths of the two squares are approximately 26.2 cm and 36 cm.
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