The Ratio of the Width, W , of the Temple $\frac { w } { h } = \frac { 2 h } { \sqrt { 5 } - 1 }$

question 110

Multiple Choice

The ratio of the width, w , of the Temple of Hephaestus to its height, h , is $\frac { w } { h } = \frac { 2 h } { \sqrt { 5 } - 1 }$ . This number is called the golden section. Early Greeks believed that the most aesthetically pleasing rectangle had this ratio. If the height is 5 , find the width. Rationalize the denominator and simplify the expression.

• A) \(\frac { 5 \sqrt { 5 } } { 2 }\)
• B) \(\frac { \sqrt { 5 } + 5 } { 2 }\)
• C) \(\frac { 5 \sqrt { 5 } - 5 } { 2 }\)
• D) \(\frac { 5 \sqrt { 5 } + 5 } { 4 }\)
• E) \(\frac { 5 \sqrt { 5 } + 5 } { 2 }\)

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Definitions:

Molecular Formula

A notation showing the types and numbers of atoms in a molecule without providing information on the arrangement or bonds between them.

Elements of Unsaturation

Indicators of the presence of double bonds, triple bonds, or rings in a molecule, which affect its hydrogen-to-carbon ratio.

Molecular Formula

A notation that shows the type and quantity of atoms in a molecule but not the bonds or arrangement.

Ring Structures

Circular arrangements of atoms within molecules that are especially common in organic chemistry.