 Hello and welcome to the session let us understand the following question today which says a ladder 5 meter 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 centimeter per second. How fast is its height on the wall decreasing when the foot of ladder is 4 meter away from the wall? Now let us see the figure for this question. Let AC be the ladder and B be the junction of the wall and ground. AB is the wall and BC is the ground and wall and ground are meeting at point B. AC is given to us as 5 meter that is the height of the ladder and let BC is equal to X and AB is equal to Y meter. Here we can see that as the point C moves away from the point B the end A also moves towards B that is X is increasing and Y is decreasing. It is given to us now that bottom of the ladder is pulled along the ground away from the wall at the rate of 2 centimeter per second that is DX by DT is equal to 2. Now let us consider the triangle ABC so here we can write X square plus Y square is equal to 25 by Pythagoras theorem. Length of the ladder is given as 10 meters so here we got 25 this can be written as X is equal to 4 so 16 plus Y square is equal to 25 which implies Y square is equal to 25 minus 16 it implies Y square is equal to 9 or Y is equal to 3 as length cannot be negative. Again we write X square plus Y square is equal to 25 now differentiating it with respect to T we get 2X DX by DT plus 2Y DY by DT is equal to 0. Now taking two common so we get X DX by DT plus Y DY by DT is equal to 0. Now substituting the values of X and Y we get 4 DX by DT plus Y is equal to 3 so 3 DY by DT is equal to 0. Also DX by DT is given to us as 2 so it implies 4 multiplied by 2 plus 3 DY by DT is equal to 0 which implies 3 DY by DT is equal to minus 8 this implies DY by DT is equal to minus 8 by 3 this negative sign implies that the height of the wall is decreasing at the rate of minus 8 by 3 centimeter per second hence the height of the wall is decreasing at the rate of 8 by 3 centimeter per second which is the required answer I hope you understood this question bye and have a nice day.