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Square ABCD and rectangle ACEG have the same area. Find the ratio AC : CE.


PS. The answer isnt 2sqrt5

 Jan 24, 2019

Draw square, start at top left corner, name corners clockwise ABCD

Draw diagonal AC as long side of rectangle, complete rectangle counterclockwise ACEG


AD = DC  call each side 1

therefore diagonal AC = sqrt2

Area of rectangle = area of square = 1

Area of rectangle = AC x CE = sqrt2 x CE

Area of rect = area of square = 1

therefore sqrt2 x CE = 1

therefore CE = 1 over sqrt2 or sqrt2 over 2

AC over CE = sqrt2 over (sqrt2 over 2) = 2sqrt2 over sqrt2 = 2 over 1

 Jan 24, 2019

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