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Ladder against a wall: find length or room width by Pythagoras

This type of question, asked 2 times: CDS 2 2019, CDS 1 2020. All 2 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 2 2019

    86
    A ladder is resting against a vertical wall and its bottom is 2.5 m away from the wall. If it slips 0.8 m down the wall, then its bottom will move away from the wall by 1.4 m. What is the length of the ladder ?

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  2. Question 2

    CDS 1 2020

    85
    A ladder 5 m long is placed in a room so as to reach a point 4.84.8 m high on a wall and on turning the ladder over to the opposite side of the wall without moving the base, it reaches a point 1.41.4 m high. What is the breadth of the room ?

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