Question

A line segment is divided in two​ segments, such that the ratio of the long segment to the short segment is equivalent to the golden ratio. If the length of the entire line segment is 15 inches​ long, what is the length of the longer piece of the divided​ segment? Use variant phialmost equals1.618.

Answer 1

9.271 inches.

Explanation:

Let AC be the length of original line segment and point B divides it into two segments such that AB is longer and BC is smaller segment.

`AB+BC=AC=15`

We can describe the golden ratio as:

`(AB)/(BC)=(AC)/(AB)=1.618`

`(AC)/(AB)=1.618`

`(15)/(AB)=1.618`

`(15)/(1.618)=AB`

`9.270704=AB`

`AB=9.271`

We can verify our answer as:

`AB+BC=15`

`9.271+BC=15`

`9.271-9.271+BC=15-9.271`

`BC=5.729`

`(AB)/(BC)=1.618`

`(9.271)/(5.729)=1.618`

`1.618=1.618`

Hence proved.

Therefore, the length of the longer side would be 9.271 inches.