A ladder leans against a wall, reaching a height of 12 meters. If the bottom of the ladder is 5 meters from the wall, how long is the ladder?
["Title: How Long Is a Ladder Reaching a Wall? A Simple Geometry Problem Explained", "When a ladder leans against a wall, its position forms a classic right triangle, with the ground, wall, and the ladder itself forming the three sides. Whether you're a student, a homeowner, or someone simply curious about geometry, understanding how to calculate the ladder’s length can be surprisingly useful—not just for physics problems, but for real-life tasks like home repairs, construction, or safety planning.", "In our example, consider a ladder resting against a vertical wall at a height of 12 meters, with its base positioned 5 meters away from the wall. The question we want to answer is: How long is the ladder? This is a perfect illustration of the Pythagorean theorem in action.", "### Understanding the Pythagorean Theorem", "The Pythagorean theorem states that in a right triangle:", "[\na^2 + b^2 = c^2\n]", "Where:\n- ( a ) and ( b ) are the lengths of the legs (the two shorter sides),\n- ( c ) is the length of the hypotenuse (the longest side, opposite the right angle), which, in this case, is the ladder’s full length.", "In our scenario:\n- The wall height (12 m) is one leg (( a = 12 )),\n- The distance from the wall (5 m) is the other leg (( b = 5 )),\n- The ladder’s length is the hypotenuse (( c = ? )).", "### Applying the Formula", "Start by substituting the known values into the Pythagorean equation:", "[\n12^2 + 5^2 = c^2\n]", "Calculate the squares:", "[\n144 + 25 = c^2\n]", "[\n169 = c^2\n]", "Now, take the square root of both sides to solve for ( c ):", "[\nc = \sqrt{169} = 13\n]", "### Conclusion: The Ladder Is 13 Meters Long", "So, if a ladder reaches 12 meters up a wall and its base is 5 meters away from the wall, the full length of the ladder must be 13 meters.", "This practical calculation not only demonstrates a foundational mathematical principle but also helps reinforce spatial reasoning and problem-solving skills. Whether you’re selecting equipment for a DIY job or verifying measurements for safety, remembering the ladder formula ensures efficiency and accuracy.", "Next time you see a ladder leaning against a wall, you’ll know it’s not just a tool—it’s a real-world example of geometry in action!", "---", "Keywords: ladder geometry, Pythagorean theorem, how long is a ladder, ladder calculation, real-world geometry, solving ladder ladder length, ladder math problem, right triangle ladder example\nMeta Description: Discover how to calculate a ladder’s length using the Pythagorean theorem. Learn with a practical example: a 12m ladder reaching 5m up a wall. Perfect for home, construction, and math practice."]
