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Vlada [557]
3 years ago
9

A line segment is divided in two​ segments, such that the ratio of the long segment to the short segment is equivalent to the go

lden 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.
Mathematics
1 answer:
vova2212 [387]3 years ago
4 0

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.

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