https://file.aiquickdraw.com/mathbot/file/1726201596615jqbv00nt.jpg

Let's solve both questions one by one:

### 10. Does the resolution 640 pixels by 480 pixels follow the Golden Ratio?

The Golden Ratio (φ) is approximately 1.618. For the monitor to follow the Golden Ratio, the ratio of the width to the height should be close to this value.

- The ratio of the monitor's resolution is:
  \[
  \text{Ratio} = \frac{640}{480} = 1.3333
  \]

Since \(1.3333\) is significantly less than \(1.618\), this monitor does **not** follow the Golden Ratio.

### 11. Calculate the width of a frame with a length of 42 inches, assuming it is a golden rectangle.

For a golden rectangle, the length (L) to width (W) follows the ratio \( \frac{L}{W} = 1.618 \). Given that the length is 42 inches:

\[
\frac{42}{W} = 1.618 \quad \Rightarrow \quad W = \frac{42}{1.618}
\]

Calculating the width:

\[
W \approx 25.95 \text{ inches}
\]

Rounding to the nearest inch, the width is approximately **26 inches**.

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Do you have any further questions or need more details? Here are some related questions to explore:

1. How does the Golden Ratio apply in design and architecture?
2. What is the derivation of the Golden Ratio from the Fibonacci sequence?
3. How would the dimensions of a rectangle differ if it followed other ratios like 4:3 or 16:9?
4. Can the Golden Ratio be applied to three-dimensional shapes?
5. How is the Golden Ratio represented in nature?

**Tip:** The Golden Ratio appears in many places in art, architecture, and nature, often seen as aesthetically pleasing proportions!

10. Older computer monitor’s resolution was 640 pixels by 480 pixels, does this monitor follow the Golden Ratio? 11. A frame has a length of 42 in. Calculate the width rounded to the nearest inch if the frame is to be a golden rectangle.

Explore whether a monitor with a 640x480 resolution follows the Golden Ratio and learn how to calculate the width of a frame with a length of 42 inches, assuming it forms a golden rectangle. This problem covers ratios and the Golden Ratio theorem, ideal for Grades 9-11.

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