305. The Ladder. As soon as the conversation turned to a ladder that was needed for some household purposes, Professor Rackbrain suddenly interrupted the discussion, offering the participants a little puzzle:

- A ladder is standing vertically against a high wall of a house. Someone pulls its lower end 4 m away from the wall. It turns out that the upper end of the ladder has dropped by $\frac{1}{5}$ of its length.

What is the length of the ladder?
305. The distance from the top end to the ground is \(\frac{4}{5}\) of the entire length of the ladder. Multiply the distance from the wall (4 m) by the denominator of this fraction (5), and you get 20. Now subtract the square of the numerator of the fraction \(\frac{4}{5}\) from the square of its denominator. This results in \(9=3^{2}\). Finally, divide 20 by 3, and you get the answer: \(6 \frac{2}{3}\) m.