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Given that the length ratio between the radii of the two circles is (2 · x) / (5 · y). The ratio of the areas of the two circles is (4 · x²) / (25 · y²).
According to the statement we know that the radius ratio between two circles. Given that the area of the circle is directly proportional to the square of its radius, then the area ratio is shown below:
A ∝ r²
A = k · r²
A' · r² = A · r'²
A' / A = r'² / r²
A' / A = (r' / r)²
A' / A = [(2 · x) / (5 · y)]²
A' / A = (4 · x²) / (25 · y²)
Given that the length ratio between the radii of the two circles is (2 · x) / (5 · y). The ratio of the areas of the two circles is (4 · x²) / (25 · y²).
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