A ladder 13 meters long leans against a wall, reaching a height of 12 meters. How far is the base of the ladder from the wall in meters?

["How Far Is the Base of a 13-Meter Ladder from the Wall When It Reaches 12 Meters High?", "When a 13-meter ladder leans against a wall, forming a right triangle with the ground, understanding the precise distance from the base to the wall is essential for both safety and practical use. If the ladder reaches a height of 12 meters, how far does its foot reach from the wall? This common geometric problem can be solved using the Pythagorean theorem — let’s break it down step by step.", "### The Geometry of the Problem", "The ladder forms the hypotenuse of a right triangle:\n- Hypotenuse (ladder length) = 13 meters\n- Vertical leg (height reached) = 12 meters\n- Horizontal leg (distance from wall to base) = unknown distance (x) meters", "According to the Pythagorean theorem:", "[\n\ ext{hypotenuse}^2 = \ ext{leg}_1^2 + \ ext{leg}_2^2\n]", "Substituting known values:", "[\n13^2 = 12^2 + x^2\n]", "[\n169 = 144 + x^2\n]", "[\nx^2 = 169 - 144 = 25\n]", "[\nx = \sqrt{25} = 5\n]", "### Conclusion", "The base of the ladder lies 5 meters from the wall. This result confirms that with a 13-meter ladder, reaching 12 meters high naturally places its base exactly 5 meters away — a perfect application of classical geometry.", "For anyone using ladders — whether for home repairs, construction, or support — this precise measurement ensures both safety and efficiency. The next time you climb out on a ladder, remember: the answer is elegantly 5 meters.", "---", "Keywords: ladder leaning against wall, how far from the wall should a 13m ladder lean, height reach calculation, right triangle ladder problem, 13 meter ladder height 12 meters, safety distance ladder, math behind ladder leaning, Pythagorean theorem ladder"]