# Differentiation and Related Rates : Rate of Change of Height and Area of a Triangle formed by a Ladder Against a House

1. A ladder is 25 feet long and is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2 feet per second. (a) How fast is the top moving down the wall when the base of the ladder is 7 feet, 15 feet and 24 feet from the wall?

(b) Consider the triangle formed by the side of the house, the ladder and the ground. Find the rate at hich the area of the triangle is changing when the base of the ladder is 7 feet from the wall.

(c) Find the rate at which the angle between the ladder and the wall of the house is changing when the base of the ladder is 7 feet from the wall.

ANSWERS: (a) - 7/12 foot per second, -3/2feet per second, -48/7 feet per second

(b) 527/24 square feet per second (c) 1/12 radian per second

#### Solution Summary

Rate of Change of Height and Area of a Triangle formed by a Ladder Against a House are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question. A diagram is included.