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

Answer:

9.271 inches.

Step-by-step 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:  

$\frac{AB}{BC}=\frac{AC}{AB}=1.618$

$\frac{AC}{AB}=1.618$

$\frac{15}{AB}=1.618$

$\frac{15}{1.618}=AB$

$9.270704=AB$

$AB=9.271$

We can verify our answer as:

$AB+BC=15$

$9.271+BC=15$

$9.271-9.271+BC=15-9.271$

$BC=5.729$

$\frac{AB}{BC}=1.618$

$\frac{9.271}{5.729}=1.618$

$1.618=1.618$

Hence proved.

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