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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
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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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