What is the length of a side of a square whose diagonal is 44 inches? 

To find the length of a side of a square given its diagonal, you can use the Pythagorean theorem. For a square, the relationship between the side length (\( s \)) and the diagonal (\( d \)) is given by:

\[
d = s\sqrt{2}
\]

Given that the diagonal is 44 inches, we can solve for \( s \):

\[
44 = s\sqrt{2}
\]

\[
s = \frac{44}{\sqrt{2}}
\]

Simplify this expression:

\[
s = \frac{44 \times \sqrt{2}}{2} = 22\sqrt{2}
\]

Now, let's calculate the numerical value of \( 22\sqrt{2} \):

\[
s \approx 22 \times 1.414 = 31.11 \text{ inches}
\]

So, the length of a side of the square is approximately **31.11 inches**.

Would you like further details, or do you have any other questions?

Here are some related questions for further exploration:

1. How do you find the diagonal of a square if you know the side length?
2. What is the formula for the perimeter of a square given the side length?
3. How does the Pythagorean theorem apply to other geometric shapes?
4. How would you find the area of a square given its diagonal?
5. How do diagonals of other polygons compare to squares?

**Tip:** The diagonal of a square always splits it into two equal right-angled triangles, making the Pythagorean theorem a handy tool!

What is the length of a side of a square whose diagonal is 44 inches?

Discover how to find the side length of a square when the diagonal measures 44 inches. Using the Pythagorean Theorem and the formula d = s√2, this problem demonstrates step-by-step how to solve for the side length. Ideal for students in Grades 7-9.

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