Solve.
-A line is subdivided according to the golden ratio, with the smaller piece having a length of 7 meters. What is the length of the entire line?
A)36.4 m
B)14 m
C)18.2 m
D)11.2 m

Question

Quizplus · Accepted Answer

The golden ratio, denoted by the Greek letter phi (φ), is approximately 1.618. When a line is divided into two parts, a and b, with a being the longer part and b the shorter part, the ratio of a to b is equal to the ratio of the sum of a and b (the whole line) to a, which is the golden ratio. Given b = 7m, we can set up the equation (a + b) / a = a / b = φ. Solving for the length of the entire line gives us approximately 18.2 meters.

Solve. -A Line Is Subdivided According to the Golden Ratio, with with the Smaller