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In a rectangle ABCD M and n are the midpoints of the sides BC and CD respectively if angle ANM is equal to 90 degrees then AB:BC is_ ?

In a rectangle ABCD M and n are the midpoints of the sides BC and CD respectively if angle ANM is equal to 90 degrees then AB:BC is_ ?

Grade:10

1 Answers

Arun
25763 Points
3 years ago
MN^2=(AB/2)^2+(BC/2)^2 
AN^2=BC^2+(AB/2)^2 
AM^2=AB^2+(BC/2)^2 

AM^2=AN^2+MN^2 
=> 
AB^2+(BC^2)/4= 
BC^2+(AB^2)/4+ 
(AB^2)/4+(BC^2)/4= 
=> 
(AB^2)/2=BC^2 
=> 
(AB/BC)^2=2 
=> 
AB:BC=sqr(2):1 

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