Suppose a square is inscribed in a circle of diameter d and another square is circumscribing the circle . Find the ratio of the area of the outer square to the area of the inner square.
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let the side of the square inscribed be x
side of square circumscribing the circle = d
as diameter of the circle = diagonal of the square
therefore diagonal = √2x = d (diagonals of a square = √2×side)
therefore d/x = √2
therefore d²/x² = √2²
ratio of areas of outer square to inner square = 2/1
side of square circumscribing the circle = d
as diameter of the circle = diagonal of the square
therefore diagonal = √2x = d (diagonals of a square = √2×side)
therefore d/x = √2
therefore d²/x² = √2²
ratio of areas of outer square to inner square = 2/1
rohanharolikar:
no prob
side of inner square = x
side of outer sqaure = d
area of square = side square, so ratio of areas = square of ratio of sides
because ratio of areas d/x = root 2, therefore ratio of areas = d^2/x^2 = [root 2]^2 = 2
did you understand
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Let the side of the square inscribed be x
side of square circumscribing the circle = d
as diameter of the circle = diagonal of the square
therefore diagonal = √2x = d (diagonals of a square = √2×side)
therefore d/x = √2
therefore d²/x² = √2²
ratio of areas of outer square to inner square = 2/1
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