I did the following SAT problem correctly using Pythagoras' Theorem and algebra, but I would like to try to do it with calculus. Is it possible to do this problem as a related rates problem?
1. A 25-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on concrete 7 feet from the base of the building. If the top of the ladder slips down 4 feet, then the bottom of the ladder will slide out ___ feet.
Let: = height of the ladder on wall
= distance of the base of the ladder to the wall
I am not sure what to substitute as x and y here.