Golden ratio

Divide line of length 14 cm into two sections that the ratio of shorter to greater is same as ratio of greater section to whole length of the line.

Result

x1 =  5.35 cm
x2 =  8.65 cm

Solution:

x1x2=x2x1+x2 x1+x2=14  x1=(21+52)14=5.35  cm \dfrac{x_1}{x_2} = \dfrac{x_2}{x_1+x_2} \ \\ x_1+x_2 = 14 \ \\ \ \\ x_1 = (2- \dfrac{1+\sqrt{5}}{2}) \cdot 14 = 5.35 \ \text{ cm }
x2=(1+521)14=8.65  cm x_2 = ( \dfrac{1+\sqrt{5}}{2}-1) \cdot 14 = 8.65 \ \text{ cm }



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