Multiple choice

A ladder of length 15 m is placed against a wall. The ground distance between the wall and the lowest point of the ladder is 9 m. Find the height where the ladder touches the wall.

  1. 10 m

  2. 11 m

  3. 12 m

  4. 15 m
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C Correct answer
Explanation

This forms a right triangle with hypotenuse 15 and base 9. Height = sqrt(15^2 - 9^2) = sqrt(225 - 81) = sqrt(144) = 12 m.

AI explanation

Applying the Pythagorean theorem to the right triangle formed by the wall, the ground, and the ladder gives the height squared plus the base squared equals the ladder's length squared. Substituting the known values results in the height squared plus 9 squared equals 15 squared, which simplifies to the height squared plus 81 equals 225. Solving for the height gives a value of 12 meters.

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