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Mathematics > Standard Multiple Choice

A -foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on concrete feet from the base of the building. If the top of the ladder slips down feet, then the bottom of the ladder will slide out

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### Explanation

The ladder, the wall, and the ground form a right triangle with a -foot hypotenuse. At first, the bottom of the ladder is feet from the base of the building, so one leg of the right triangle measures feet; the length of the other leg, , can be found by solving , which is the Pythagorean theorem. From this, you can figure out that the other leg measures feet.

After the ladder slips down feet, the -foot leg of the right triangle becomes feet long. The other leg then has to be feet long. This length is found by solving , which is again the Pythagorean theorem.

Since the distance between the bottom of the ladder and the base of the building increases from feet to feet, the amount that the bottom of the ladder slides out is feet.