2026 MSHS P1 Q11

A ladder of fixed length 10 m leans against a vertical wall. The base of the ladder slides away from the wall along the horizontal ground. At time \(t\) seconds, the base of the ladder is \(x\) m from the wall, and the height the ladder reaches up the wall is \(h\) m. The base of the ladder is sliding away from the wall at a constant rate of 0.5 m per second.

1. Show that \(h\) is decreasing at a constant rate of 0.375 m per second when \(x=6\).[5]
2. Find the rate of change of the area of the triangle formed by the ladder, the wall and the ground with respect to \(t\) when \(x=6\).[3]