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Ladder Against Wall Height Calculation

CMAT 2022 · Quantitative Techniques & Data Interpretation · Easy · Trigonometry

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If a 30 meter ladder is placed against a wall such that it just reaches the top of the wall, and the horizontal distance between the wall and the base of the ladder is 1/3rd of the length of ladder, then the height of the wall is:

  1. A.

    25 meter

  2. B.

    20\sqrt{2} meter

  3. C.

    20\sqrt{3} meter

  4. D.

    20 meter

Answer

B

Explanation

Length of ladder (hypotenuse) c=30 mc = 30\text{ m}. Base b=13×30=10 mb = \frac{1}{3} \times 30 = 10\text{ m}. By Pythagoras theorem, h2+b2=c2h^2 + b^2 = c^2. h2+102=302  ⟹  h2=900−100=800h^2 + 10^2 = 30^2 \implies h^2 = 900 - 100 = 800. h=800=202 mh = \sqrt{800} = 20\sqrt{2}\text{ m}.

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