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.
Pythagoras Theorem
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Question

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.

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KnowledgeBoat · Accepted Answer

First ladder reaches at A, thus AB = 4 m and AC = 5 m.

Given,

Foot of the ladder is moved 1.6 m towards the wall

The distance by which the top of the ladder would slide upwards on the wall = AE

By Pythagoras theorem,

Hypotenuse² = Perpendicular² + Base²

In triangle ABC,

⇒ AC² = AB² + BC²

⇒ 5² = 4² + BC²

⇒ 25 = 16 + BC²

⇒ BC² = 25 - 16

⇒ BC² = 9

⇒ BC = $\sqrt{9}$

⇒ BC = 3 m

BD = BC - CD = 3 - 1.6 = 1.4 m

In triangle EBD,

Ladder ED = 5 m

⇒ ED² = EB² + BD²

⇒ 5² = EB² + (1.4)²

⇒ 25 = EB² + 1.96

⇒ EB² = 25 - 1.96

⇒ EB² = 23.04

⇒ EB = $\sqrt{23.04}$

⇒ EB = 4.8 m

From figure,

AE = EB - AB = 4.8 - 4 = 0.8 m

Hence, the distance by which the top of the ladder would slide upwards on the wall is 0.8 m.