Multiple choice

A ladder is leaning against the wall. The top of the ladder touches the wall at a height of 15 m. If the length of the ladder is 1 m more than twice its distance from the wall, find the distance from the wall to the bottom of ladder.

  1. 14 m

  2. 12 m

  3. 9 m

  4. 8 m
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let distance from wall be x. Ladder length L = 2x + 1. Height = 15. By Pythagoras: x^2 + 15^2 = (2x + 1)^2. x^2 + 225 = 4x^2 + 4x + 1. 3x^2 + 4x - 224 = 0. Using quadratic formula: x = (-4 + sqrt(16 - 4*3*(-224))) / 6 = (-4 + sqrt(16 + 2688)) / 6 = (-4 + 52) / 6 = 48 / 6 = 8.

AI explanation

Let the distance from the wall be x, so the ladder length is 2x + 1. Using the Pythagorean theorem with the wall height gives x squared + 15 squared = (2x + 1) squared. Expanding and rearranging this gives 3x squared + 4x - 224 = 0, which factors to (3x + 28)(x - 8) = 0. Discarding the negative result leaves x = 8.

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