A ladder 5 m long leans against a vertical wall. The bottom of the ladder is 3 m from the wall. If the bottom of the ladder is pulled 1 m farther from the wall, how much does the top of the ladder slide down the wall
Step-by-Step Solution
Key Concept: Using the Pythagorean theorem in right triangles to find missing sides, then subtracting to find the required distance.
From the first case, triangle $ABC$ has $AB = 4$ m (height), $BC = 3$ m (base), and $AC = 5$ m (hypotenuse). From the second case, triangle $DBC'$ has $BD$ perpendicular to $BC'$, with $BC' = 4$ m and $DC' = 5$ m (hypotenuse). Using the Pythagorean theorem: $BD^2 + BC'^2 = DC'^2$, we get $BD^2 + 16 = 25$, so $BD = 3$ m. Therefore, $AD = AB - BD = 4 - 3 = 1$ m.
Correct Answer: 1