If a line is divided into 2 parts with the lengths of larger one and smaller one as "a" and " b" respectively. Then ,

which of the following must be true to get the golden ratio 1.618 ?

a) $\frac{a + b}{a} = \frac{b}{a}$

b) $\frac{a + b}{a} = \frac{a}{b}$

c) $\frac{a b + b}{a} = \frac{b}{a}$

d) $\frac{a + b}{a} = \frac{a b}{a}$

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Solution

The correct option is B
b)

$\frac{T o t a l l e n g t h o f t h e l i n e}{l e n g t h o f t h e l a r g e r p a r t}$ and $\frac{l e n g t h o f t h e l a r g e r p a r t}{l e n g t h o f t h e s h o r t e r p a r t}$ must be equal to the golden ratio value 1.618.

So, answer is $\frac{a + b}{a} = \frac{a}{b}$ .

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