Multiple choice

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

  1. 25 metres

  2. 20 2 metres

  3. 20 3 metres

  4. 20 metres
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The horizontal distance is 30/3 = 10 metres. By the Pythagorean theorem, the wall height is sqrt(30^2 - 10^2) = sqrt(800) = 20sqrt(2) metres, so option B is correct.

AI explanation

The wall, the ground, and the ladder form a right triangle where the ladder is the hypotenuse. The horizontal distance is one-third of the ladder's length, making it 10 meters. Using the Pythagorean theorem, the height of the wall squared equals the hypotenuse squared minus the base squared, which is 30 squared minus 10 squared, or 900 minus 100. The height of the wall is therefore the square root of 800, which simplifies to 20 times the square root of 2 meters.

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