#### 21. A ladder is leaning against a wall, forming a right triangle with the ground. The ladder is 13 meters long, and its base is 5 meters from the wall. How high up the wall does the ladder reach?

Tue, 05 May 2026 21:41:35 +0000

### 21. A ladder is leaning against a wall, forming a right triangle with the ground. The ladder is 13 meters long, and its base is 5 meters from the wall. How high up the wall does the ladder reach? Ever wondered why certain visual patterns—like a sturdy ladder leaning against a wall—quickly appear in online searches and sideline discussions? Often rooted in curiosity about physics, math, or DIY problem-solving, this simple triangle puzzles everyday minds seeking tangible answers. The scenario—13 meters of ladder, 5 meters base from the wall—sets the stage for a classic geometry question that blends real-world application with fundamental numeric logic. When a ladder rests against a vertical wall, it forms a right triangle: the ladder acts as the hypotenuse, the wall’s height as one leg, and the ground distance as the other. With known values—the hypotenuse (13 m) and adjacent leg (5 m)—math guides us precisely. This helps explain not just how high the ladder reaches, but reinforces how basic geometry applies to common tasks like home repairs, moving furniture, or installing installations. Let’s break it down clearly. We use the Pythagorean theorem: a² + b² = c², where c is the hypotenuse, a is the base, and b is the unknown height. Substituting: 5² + b² = 13² → 25 + b² = 169. Subtract 25: b² = 144. Taking the square root, b = 12. So, the ladder reaches 12 meters high on the wall.