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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:10

1 Answers

Shyama P
35 Points
9 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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