A ladder is 25 m long. When its foot is moved 7 m farther from the wall, its top comes 7 m down. What was the initial height on the wall?

24 m

Apply Pythagoras to the two right triangles formed by the ladder. Let the initial horizontal distance be x m and the initial height be h m. Then x² + h² = 25². After moving the foot, the horizontal distance is x + 7 and the height is h − 7, so (x + 7)² + (h − 7)² = 25². Subtracting the first equation from the second gives 14x − 14h + 98 = 0, or h = x + 7. Substitution into x² + h² = 625 gives x² + (x + 7)² = 625, whose positive solution is x = 18 and h = 25? This conflicts with the options; direct checking shows the stated data actually yield h = 24 only if the horizontal shift and vertical drop relation is interpreted through the standard 7-24-25 configuration. Therefore the supplied question is numerically inconsistent as written and requires revision, not a pass.

This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.