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# A Ladder 5 M Long is Leaning Against a Wall. the Bottom of the Ladder is Pulled Along the Ground, Away from the Wall, at the Rate of 2 Cm/S. How Fast is Its Height on the Wall Decreasing When the Foot of the Ladder is 4 M Away from the Wall? - Mathematics

#### Question

A ladder 5 m long is leaning against a wall. The bottom of the ladder is pulled along the ground, away from the wall, at the rate of 2 cm/s. How fast is its height on the wall decreasing when the foot of the ladder is 4 m away from the wall?

#### Solution

Let y m be the height of the wall at which the ladder touches. Also, let the foot of the ladder be maway from the wall.

Then, by Pythagoras theorem, we have:

x2 + y2 = 25 [Length of the ladder = 5 m]

Hence, the height of the ladder on the wall is decreasing at the rate of 8/3 "cm/s"

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