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The problem states:

- The fabric panels on a kite are rhombuses.
- The formula for the length of the long diagonal \( d \) is given by:
  \[
  d = s \sqrt{3}
  \]
  where \( s \) is the length of a side.
  
### Part 1: Solve for \( s \)
We are asked to solve the formula for \( s \).

The given formula is:
\[
d = s \sqrt{3}
\]
To isolate \( s \), divide both sides by \( \sqrt{3} \):
\[
s = \frac{d}{\sqrt{3}}
\]

### Part 2: Find the value of \( s \) when \( d = 15 \) inches
Now, substitute \( d = 15 \) into the formula:
\[
s = \frac{15}{\sqrt{3}}
\]
To simplify this, multiply the numerator and the denominator by \( \sqrt{3} \):
\[
s = \frac{15 \sqrt{3}}{3} = 5 \sqrt{3}
\]
Thus, the length of a side is \( s = 5 \sqrt{3} \) inches.

If you want to approximate it:
\[
s \approx 5 \times 1.732 = 8.66 \text{ inches}
\]

### Summary
- The side length \( s \) is \( 5 \sqrt{3} \) inches, which is approximately 8.66 inches.

Would you like more details or have any other questions?

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Here are 5 related questions you might find useful:
1. What is the formula for the short diagonal of a rhombus?
2. How can the Pythagorean theorem be used in kite designs?
3. How does the area of a rhombus relate to its diagonals?
4. What are the geometric properties of a kite in terms of symmetry and diagonals?
5. How do you convert between exact form (with roots) and decimal approximations in geometry?

**Tip:** When simplifying expressions with square roots, multiplying both the numerator and denominator by the square root helps to rationalize the denominator.

The fabric panels on a kite are rhombuses. A formula for the length of the long diagonal d is d = s√3 where s is the length of a side. Solve the formula for s. Then find the value of s when d = 15 inches.

Learn how to solve for the side length of a rhombus when given the length of the diagonal using the formula d = s√3. This geometry problem covers algebraic manipulation and square roots, suitable for students in Grades 8-10. Example: Find s when d = 15 inches.

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