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

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) $\frac { 5 \sqrt { 5 } + 5 } { 2 }$