A 5 m long ladder is placed leaning towards a vertical wall such that it reaches the wall at a point 4 m high. If the foot of the ladder is moved 1.6 m towards the wall, then find the distance by which the top of the ladder would slide upwards on the wall
Solution:
Given, length of ladder = 5 m
The ladder is placed leaning towards a vertical wall such that it reaches the wall at a point 4 m high.
We have to find the distance by which the top of the ladder would slide upwards on the wall if the foot of the ladder is moved 1.6 m towards the wall.
From the figure,
DL is the length of the ladder = 5 m
LW is the height of the wall at which the ladder is placed = 4 m
DW is the distance between the foot of the ladder to the wall
DR is the distance at which the foot of ladder is moved towards the wall = 1.6 m
EL is the distance that the ladder slides upwards..
In △DLW,
DLW is a right triangle with W at right angles.
DL2 = DW2 + LW2
(5)2 = DW2 + (4)2
DW2 = 25 - 16
DW2 = 9
Taking square root,
DW = 3 m
From the figure,
RW = DW - DR
RW = 3 - 1.6
RW = 1.4 m
In △REW,
By pythagoras theorem,
RE2 = RW2 + EW2
(5)2 = (1.4)2 + EW2
EW2 = 25 - 1.96
EW2 = 23.04 m
Taking square root,
EW = 4.8 m
Now, EW = LE + LW
4.8 = EL + 4
EL = 4.8 - 4
EL = 0.8 m
Therefore, the distance by which the top of the ladder would slide upwards on the wall if the foot of the ladder is moved 1.6 m towards the wall is 0.8 m
✦ Try This: A ladder, 5 meter long, standing on a horizontal floor, leans against a vertical wall. If the top of the ladder slides downwards at the rate of 10cm/sec, then find the rate at which the angle between the floor and the ladder is decreasing when the lower end of the ladder is 2 meters from the wall.
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 6
NCERT Exemplar Class 10 Maths Exercise 6.4 Problem 5
A 5 m long ladder is placed leaning towards a vertical wall such that it reaches the wall at a point 4 m high. If the foot of the ladder is moved 1.6 m towards the wall, then find the distance by which the top of the ladder would slide upwards on the wall
Summary:
A 5 m long ladder is placed leaning towards a vertical wall such that it reaches the wall at a point 4 m high. If the foot of the ladder is moved 1.6 m towards the wall, then the distance by which the top of the ladder would slide upwards on the wall is 0.8 m
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