The shorter side of a golden rectangle is 7 inches. How long is the longer side?

In a golden rectangle, the ratio of the longer side to the shorter side is the golden ratio, which is approximately \( \phi \approx 1.618 \).

Given that the shorter side is 7 inches, we can find the length of the longer side by multiplying 7 inches by the golden ratio:

\[
\text{Longer side} = 7 \times 1.618 \approx 11.326 \, \text{inches}.
\]

So, the longer side is approximately **11.33 inches**.

Would you like more details or have any questions?

Here are 5 related questions to explore:

1. How is the golden ratio derived mathematically?
2. What are some applications of the golden ratio in real life?
3. How can you construct a golden rectangle geometrically?
4. What is the difference between a golden rectangle and a regular rectangle?
5. How does the Fibonacci sequence relate to the golden ratio?

**Tip:** The golden ratio appears in many natural

Discover how to find the length of the longer side of a golden rectangle when the shorter side is 7 inches. This problem explores geometry concepts like the golden ratio and its application in proportions, making it ideal for students in Grades 9-12.

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