A square and a circle have the same perimeter. If the side of the square is 10 units, what is the radius of the circle? (Use \( \pi \approx 3.14 \))

["Perfect Geometry Match: How a Square and Circle Share the Same Perimeter", "When exploring the world of geometry, one fascinating fact is that a square and a circle can have identical perimeters—even when their shapes differ completely. This concept not only highlights the elegance of mathematical relationships but also helps solve real-world problems involving boundaries and space.", "Understanding the Perimeter: Square vs. Circle", "The perimeter of a square is calculated easily using the formula:\nPerimeter = 4 × side\nIf the side of the square is 10 units, then:\n[\n\ ext{Perimeter} = 4 \ imes 10 = 40 \ ext{ units}\n]", "For a circle, the perimeter (also called circumference) is given by:\nCircumference = 2 × π × radius\nSince we know the circumference equals 40 units, we set up the equation:\n[\n2 \pi r = 40\n]\nUsing ( \pi \approx 3.14 ), substitute and solve for the radius ( r ):\n[\n2 \ imes 3.14 \ imes r = 40\n]\n[\n6.28r = 40\n]\n[\nr = \frac{40}{6.28} \approx 6.37 \ ext{ units}\n]", "So, if a square has a side of 10 units, the circle with the same perimeter must have a radius of approximately 6.37 units.", "Why This Matters", "This relationship between shapes is not just theoretical—it applies in engineering, architecture, and manufacturing where space optimization is key. Understanding how to equate perimeters helps in designing efficient structures, minimizing materials, or comparing surface boundaries regardless of shape.", "In Summary:\n- A square with side 10 units has a perimeter of 40 units.\n- A circle with the same perimeter must have a radius calculated as ( r = \frac{Perimeter}{2\pi} \approx 6.37 ) units.\n- This demonstrates how different geometric figures can relate perfectly through shared measurements.", "By mastering such principles, you unlock deeper insights into geometry and its practical applications in everyday life. Whether for study, work, or curiosity, knowing the connection between a square’s side and a circle’s circumference is both elegant and useful."]