A ladder 13 meters long leans against a wall, with its base 5 meters from the wall. How high up the wall does the ladder reach?
["How High Does a 13-Meter Ladder Reach When Leaning Against a Wall at 5 Meters Away?", "When you’re trying to solve a basic physics problem involving a ladder leaning against a wall, the relationship between the ladder’s length, distance from the wall, and the height it reaches is governed by the Pythagorean theorem—a fundamental principle in geometry. In this article, we’ll walk through how to calculate the maximum height a 13-meter-long ladder achieves when its base is placed 5 meters away from a vertical wall.", "---", "### The Setup: Distance and Ladder Length", "Imagine a straight, sturdy ladder stretched at exactly 13 meters from the base of a wall to the top. The bottom of the ladder is securely positioned 5 meters away from the wall. The key question is: How high up the wall does this ladder reach?", "This scenario forms a right triangle, where:\n- The ladder is the hypotenuse (13 meters),\n- The distance from the wall to the ladder’s base is one leg (5 meters),\n- The height up the wall is the other leg (the unknown we seek).", "---", "### Applying the Pythagorean Theorem", "The Pythagorean theorem states:", "[\n\ ext{Hypotenuse}^2 = \ ext{Leg}_1^2 + \ ext{Leg}_2^2\n]", "Substituting known values:", "[\n13^2 = 5^2 + h^2\n]", "Calculate each square:", "[\n169 = 25 + h^2\n]", "Subtract 25 from both sides:", "[\nh^2 = 169 - 25 = 144\n]", "Now take the square root:", "[\nh = \sqrt{144} = 12\n]", "---", "### Result: The Ladder Reaches 12 Meters Up the Wall", "With the base 5 meters from the wall and the full ladder length of 13 meters, the maximum height the ladder reaches on the wall is 12 meters.", "---", "### Why This Matters", "Understanding this calculation helps with safe ladder use—common in construction, cleaning, and home improvement. A properly positioned ladder prevents slipping and ensures the ladder reaches a safe working height without compromising stability.", "---", "### Summary", "- Ladder length = 13 m (hypotenuse)\n- Distance from wall = 5 m (one leg)\n- Height of climb = 12 m (other leg)\n- Mathematical proof: ( 13^2 = 5^2 + 12^2 ) → ( 169 = 25 + 144 ) → valid", "This classic setup confirms that a 13-meter ladder leaning 5 meters from a wall reaches a height of 12 meters, thanks to the reliable math of geometry.", "---", "Keywords for SEO:\nladder height calculation, ladder leaning against wall, Pythagorean theorem ladder, how high does a 13-meter ladder reach, ladder safety tips, right triangle ladder problem, wall ladder height formula", "Meta Description:\nDiscover how high a 13-meter ladder reaches when placed 5 meters from a wall using the Pythagorean theorem. Learn the step-by-step geometry behind this common problem."]
