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In a rectangle ABCD , M and N are the midpoints of sides BC and CD respectively.if angle ANM=90 degree, then AB:BC=? A)ROOT 2 :1 B)2:1 C)ROOT 3:1 D)3:1

In a rectangle ABCD , M and N are the midpoints of sides BC and CD respectively.if angle ANM=90 degree, then AB:BC=?
A)ROOT 2 :1
B)2:1
C)ROOT 3:1
D)3:1

Grade:10

1 Answers

Arun
25750 Points
6 years ago
Dear Devika
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
Hence option A is correct.
Regards
Arun (askIITians forum expert)

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