Top of the ladder slides down a vertical wall at a constant rate of 0.15 m/s.

Bottom of the ladder is 3 m away from the wall.

Bottom of the ladder slides away at a rate of 0.2 m/s.

Let  is the length of the ladder.

 is the distance between the bottom of the ladder and wall is  m.

 is the shortest distance from the top of the ladder to ground.

Ladder slides on the ground at a rate of change is  m/s.

The ladder slides down vertical at a rate of change  m/s.

From Pythagoras theorem,

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Differentiate on each side with respect to .

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Length of the ladder is constant.

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.

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Substitute ,  and  in above equation.

Length of the ladder m.

Length of the ladder m.