Answer
$\frac{w}{h} = \frac{\sqrt 5 + 1}{2}$
Work Step by Step
$ \frac{w}{h}$ = $\frac{2}{\sqrt 5 - 1}$
To rationalize the denominator multiply the numerator and denominator by the conjugate of the denominator. The conjugate of the denominator $\sqrt 5 - 1 $ is $\sqrt 5 + 1 $
= $\frac{2}{\sqrt 5 - 1}$ $\times$ $\frac{\sqrt 5 + 1}{\sqrt 5 + 1}$
= $ \frac{2(\sqrt 5 + 1)}{(\sqrt 5 -1)(\sqrt 5 + 1)}$
$( \sqrt a - \sqrt b)( \sqrt a + \sqrt b)$ = $ (\sqrt a)^{2}$ - $ (\sqrt b)^{2}$. Therefore,
$( \sqrt 5- 1)( \sqrt5 +1)$ = $ (\sqrt5)^{2}$ - $ (1)^{2}$.
$= \frac{2(\sqrt 5 + 1)}{ (\sqrt5)^{2} - (1)^{2}}$
$= \frac{2(\sqrt 5 + 1)}{ (5 - 1)}$
$= \frac{2(\sqrt 5 + 1)}{4}$
$ = \frac{2}{4} \times (\sqrt 5 + 1)$
$\frac{w}{h}= \frac{\sqrt 5 + 1}{2}$
$\sqrt 5 \approx 2.2361$
$\frac{w}{h}= \frac{2.2361 + 1}{2}$
$\frac{w}{h}= \frac{3.2361}{2} = 1.61805$
$\frac{w}{h}= 1.62$ (to nearest hundredth)
$\frac{w}{h}= \frac{1.62}{1}$
Ratio of width to height is 1.62 to 1
