Diagonal = √(12² + 8²) = √(144 + 64) = √208 ≈ <<sqrt(208)=14.4>>14.4 meters.

["Diagonal Calculation Explained: Diagonal = √(12² + 8²) ≈ 14.4 Meters", "When working with rectangles, determining the length of the diagonal is essential for everything from construction and interior design to simple measurements around the home. One common formula used to calculate this diagonal is:", "[\n\ ext{Diagonal} = \sqrt{a^2 + b^2}\n]", "where ( a ) and ( b ) are the lengths of the rectangle’s sides. In this example, we use the side lengths of 12 meters and 8 meters. Applying the formula step-by-step offers both clarity and precision.", "---", "### Step-by-Step Breakdown", "Start with the known dimensions:\n- Side ( a = 12 ) meters\n- Side ( b = 8 ) meters", "Calculate the squares:", "[\n12^2 = 144\n]\n[\n8^2 = 64\n]", "Add the squared values:", "[\n144 + 64 = 208\n]", "Now take the square root to find the diagonal:", "[\n\sqrt{208} \approx 14.4\n]", "This means the diagonal measures approximately 14.4 meters — a straightforward yet powerful application of the Pythagorean theorem.", "---", "### Why This Formula Matters", "In real-world applications, such as framing a room, laying tile, or positioning furniture across a corner, knowing the true diagonal length ensures accuracy and prevents material waste. The expression:", "[\n\boxed{\ ext{Diagonal} = \sqrt{12^2 + 8^2} = \sqrt{208} \approx 14.4 \ ext{ meters}}\n]", "is both mathematically sound and highly practical.", "---", "### Pro Tip: Simplifying √208", "If precision matters, √208 can be simplified:", "[\n\sqrt{208} = \sqrt{16 \ imes 13} = 4\sqrt{13} \approx 4 \ imes 3.605 = 14.42 \ ext{ (approx.)}\n]", "While 14.4 is sufficient for most practical purposes, converting to irrational form offers deeper insight.", "---", "### Conclusion", "Calculating the diagonal using ( \sqrt{a^2 + b^2} ) is a fundamental geometric skill. Whether you’re building a shelf, laying out a floor, or solving a simple math problem, knowing how to compute diagonals accurately empowers better decision-making and precision — all from a clear, computational basis.", "Keywords: diagonal calculation, Pythagorean theorem, √208, rectangle diagonal formula, measure diagonal meters, geometry practice, math tutorial, home improvement measurement."]