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

Sun, 03 May 2026 18:32:56 +0000

**How Far Is the Base of a 13-Meter Ladder From the Wall When It Reaches 12 Meters High?**
A simple geometry question that’s drawing quiet attention in the US—especially among homeowners, renters, DIY builders, and those learning basic physics. The problem is: A 13-meter-long ladder leans against a wall, reaching exactly 12 meters high. But where does the ladder’s base land from the wall? The answer isn’t obvious at first—but with a little math, the solution becomes clear and reassuring. Understanding how ladders stabilize involves basic principles of right triangles. When a ladder leans against a wall, it forms a right triangle with the wall (vertical side), the ground (horizontal base), and the ladder itself as the hypotenuse. Known values are: hypotenuse = 13 meters, vertical leg = 12 meters. The unknown—distance from wall to ladder base—is the horizontal leg. Using the Pythagorean theorem (a² + b² = c²), you set up the equation:
Base² + 12² = 13²
Base² + 144 = 169
Base² = 169 – 144
Base² = 25
Base = √25 = 5 meters So the ladder’s base is exactly 5 meters from the wall.