## 299. Math Puzzle $4 / 90$

Curiously, Jaqueline looks over her older brother's shoulder as he is studying. She wants to know what the "Golden Ratio" is all about.

Marco explains to her that proportions in architecture and other design fields often have special significance based on this principle:

"A line is divided into two segments in the Golden Ratio if the smaller segment is to the larger segment as the larger segment is to the sum of both segments."

To be able to continue studying undisturbed, Marco lets his sister figure out how wide a $1.50 \mathrm{~m}$ high window must be if the width and height are to be in the Golden Ratio. Can you help Jaqueline solve this?
$$
\frac{\text { Width }}{\text { Height }}=\frac{\text { Height }}{\text { Width }+ \text { Height }} \quad, \quad \text { Width }=\text { Height }\left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \approx 0.92
$$

The window must be approximately $92 \mathrm{~cm}$ wide.