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If the sides of triangle ABC are in G.P ...

If the sides of triangle `ABC` are in G.P with common ratio `r (r<1)`, show that `r<1/2(sqrt5+1)`

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it is given that a,b,c are in GP
a=1, b=r, c=`r^2`
sum of two sides is always greater than the third side
(a+b)>c
(1+r)>`r^2`
`r^2-r-1<0`
r=`(1+-sqrt(1+4))/2`
r=`(1+-sqrt(5))/2`
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