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3 years ago

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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.

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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