The length of a diagonal of a square is 10 cm. What is the perimeter of the square?
["The Length of a Diagonal of a Square is 10 cm: How to Calculate the Perimeter", "Understanding the relationship between the diagonal and the perimeter of a square is a fundamental aspect of geometry. Whether you're designing architecture, solving math problems, or just curious about shapes, knowing how to find the perimeter from the diagonal can be incredibly useful. In this article, we’ll explore how to calculate the perimeter when the diagonal of a square is 10 cm.", "---", "### What is the Length of the Diagonal of a Square?", "For a square with side length ( s ), the length of the diagonal ( d ) is determined using the Pythagorean theorem. Since the diagonal splits the square into two right-angled triangles:", "[\nd = s\sqrt{2}\n]", "Given ( d = 10 ) cm, we solve for ( s ):", "[\ns\sqrt{2} = 10 \Rightarrow s = \frac{10}{\sqrt{2}} = \frac{10\sqrt{2}}{2} = 5\sqrt{2} \ ext{ cm}\n]", "---", "### How to Calculate the Perimeter from the Diagonal", "The perimeter ( P ) of a square is simply four times the side length:", "[\nP = 4s\n]", "Substituting ( s = 5\sqrt{2} ):", "[\nP = 4 \ imes 5\sqrt{2} = 20\sqrt{2} \ ext{ cm}\n]", "---", "### Approximate Numerical Value", "To help visualize better, ( \sqrt{2} \approx 1.414 ), so:", "[\nP \approx 20 \ imes 1.414 = 28.28 \ ext{ cm}\n]", "---", "### Final Answer", "If the diagonal of a square is 10 cm, the perimeter of the square is:", "[\n\boxed{20\sqrt{2} \ ext{ cm}} \quad (\ ext{approximately } 28.28 \ ext{ cm})\n]", "---", "### Summary", "- The diagonal of a square with side ( s ) is ( s\sqrt{2} )\n- When diagonal = 10 cm, side ( s = 5\sqrt{2} ) cm\n- Perimeter = ( 4s = 20\sqrt{2} ) cm (exact) or about 28.28 cm (approximate)\n- This knowledge helps in practical applications like construction, art, and geometry problems", "Understanding these formulas allows you to effortlessly switch between diagonal and perimeter measurements—key for many real-world and academic pursuits."]
