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if the length of diagonal of regular pentagon is b and side length is a,prove that a^2/b^2+b^2/a^2=3

if the length of diagonal of regular pentagon is b and side length is a,prove that a^2/b^2+b^2/a^2=3 

Grade:11

1 Answers

Arun
25750 Points
3 years ago
 
consider right triangle AOB
 
angle OAB =54 degree
 
sin54=b/2a
 
b=2asin54
 
sub in eq.
 
a2/(4a2sin254) + (4a2sin254)/a2 =3

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