A ladder 13 meters long leans against a wall, reaching a height of 12 meters. How far is the base from the wall?
["How Far Is the Base of a 13-Meter Ladder from the Wall When It Reaches 12 Meters High?", "When you’re trying to safely position a ladder, knowing the right geometry can prevent accidents and ensure stability. A common real-life scenario involves a 13-meter-long ladder reaching up to 12 meters on a wall. But exactly how far should the base be placed from the wall? This article breaks down the physics and math behind the problem.", "### The Setup: A Right Triangle in Disguise", "Imagine the ladder as the hypotenuse of a right triangle:\n- The ladder itself (13 meters) = hypotenuse.\n- The vertical height it reaches on the wall (12 meters) = one leg of the triangle.\n- The distance from the base of the ladder to the wall = other leg (what we’re solving for).", "Let:\n- ( c = 13 ) meters (ladder length, the hypotenuse),\n- ( a = 12 ) meters (height on wall),\n- ( b = ? ) meters (distance from wall, unknown leg).", "Using the Pythagorean Theorem:", "[\nc^2 = a^2 + b^2\n]", "Substitute known values:", "[\n13^2 = 12^2 + b^2\n]", "[\n169 = 144 + b^2\n]", "[\nb^2 = 169 - 144 = 25\n]", "[\nb = \sqrt{25} = 5\n]", "### Answer: The base of the ladder is 5 meters from the wall.", "### Why This Matters", "This layout ensures the ladder forms a stable triangle, distributing weight safely and minimizing slipping risk. Placing the base 5 meters from the wall allows optimal balance—closer would risk leaning too steeply, and farther reduces efficiency.", "### Bonus Tips for Ladder Safety\n- Use the 4:1 Rule: For every 4 meters up the wall, place the base 1 meter from the wall (e.g., 12 meters high → base 3 meters out gives ideal stability at ~5 meters, exactly matching our calculation).\n- Always check ladder stability and wall condition.\n- Avoid overreaching, which tilts the ladder and increases fall risk.", "---", "Keywords: ladder safety, 13 meter ladder, how far is ladder base from wall, right triangle ladder problem, ladder positioning physics, wall anchor distance formula."]
