Respuesta :
The length which result in a ratio closest to the golden ratio is equal to 7.5 inches and 4.5 inches. Option C is correct.
What is the length of line segment?
The line segment is made with two end points. Length of a line segment is the distance of both the ends of it.
A 12 inch line segment is divided into two parts. Suppose the line segment is AC which is divided into AB and BC parts. Thus,
AB+BC=AC
AB+BC=12 ....1
The value of golden ratio is equal to 1.618. It can also be given as (1+√5)/2. The ratio of both segment is equal to golden ratio. Thus
[tex]\dfrac{AB}{BC}=\dfrac{AC}{AB}=\dfrac{1+\sqrt{5}}{2}\\\dfrac{12}{AB}=1.618\\AB=7.4166 \rm\; in[/tex]
Put this value in equation one as,
AB+7.4166=12
AB=4.5834
The length which result in a ratio closest to the golden ratio is equal to 7.5 inches and 4.5 inches. Option C is correct.
Learn more about the line segment here;
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