Rectangle ACEF shown in the figure is a golden rectangle. It is constructed from square ACDB by holding line segment OB fixed at point O an then letting point B drop down until OB aligns with CD. The ratio of the length to the width in the golden rectangle is called the golden ratio. Find the lengths below to arrive at the golden ratio. (Let a = 1.)

(a) Find the length of OB.
OB = ______
(b) Find the length of OE.
OE = ______
(c) Find the length of CE.
CE = ______
(d) Find the ratio .

= ______

Question

Rectangle ACEF shown in the figure is a golden rectangle. It is constructed from square ACDB by holding line segment OB fixed at point O an then letting point B drop down until OB aligns with CD. The ratio of the length to the width in the golden rectangle is called the golden ratio. Find the lengths below to arrive at the golden ratio. (Let a = 1.)

(a) Find the length of OB.
OB = ______
(b) Find the length of OE.
OE = ______
(c) Find the length of CE.
CE = ______
(d) Find the ratio .
 
= ______

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