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FBA2aaaECOD(a) Find the length of OBV5OB =(b) Find the length of OEV5OE =(c) Find the length of CE.1 5CE =X(d) Find the ratio CEEF1CEEF2

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 and 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 = 4.)

F
B
A
2a
a
a
E
C
O
D
(a) Find the length of OB
V5
OB =
(b) Find the length of OE
V5
OE =
(c) Find the length of CE.
1 5
CE =
X
(d) Find the ratio CE
EF
1
CE
EF
2
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F B A 2a a a E C O D (a) Find the length of OB V5 OB = (b) Find the length of OE V5 OE = (c) Find the length of CE. 1 5 CE = X (d) Find the ratio CE EF 1 CE EF 2

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Step 1

According to given figure :

The l...

OB a +(2a
= va +4a
= a5 (a=4)
4/5
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OB a +(2a = va +4a = a5 (a=4) 4/5

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Trigonometric Ratios

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