+41 Square ABCD and rectangle ACEG have the same area. Find the ratio AC : CE.
PS. The answer isnt 2sqrt5
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
