Homework SourseA ladder 25 feet long is leaning against the wall of a house
A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2 ft per sec. Consider the triangle formed by the side of the house, the ladder, and the ground. Find the rate at which the area of the triangle is changed when the base of the ladder is 11 feet from the wall. I need all work to be shown! Please help asap! Will give an awesome rating for detailed work!
Solution
let distance of ladder\'s foot from the wall = x height of point at which ladder touches the wall = y x^2 + y^2 = 25^2 = 625 differentiate w.r.t t on both sides 2xdx/dt + 2ydy/dt = 0 dx/dt / dy/dt = -y/x when x = 11, y= 22.45 ft dx/dt = 2 dy/dt = -0.98 ft/s area = 1/2 xy dA/dt = 1/2 * (xdy/dt + ydx/dt) = 17.06 ft^2 /s
