Question

A ladder 13 feet long is leaning against the side of a building. If the foot of the ladder is pulled away from the building at a constant rate of 8 inches per second, how fast is the area of the triangle formed by the ladder, the building and the ground changing (in feet squared per second ) at the instant when the top of the ladder is 12 feet above the ground?

Answer 1

Step 1:

Length of the ladder as feet.

Figure illustration of the problem:

Foot of the ladder slides away from the building at a rate of change is inches per second.

 feet per second.

From the Pythagorean theorem:

Substitute in above expression.

Find value at  feet .

Step 2:

Differentiate with respect to  on each side.

Substitute corresponding values , x = 5 and in above expression to find  .

Step 3:

Area of the triangle .

Differentiate with respect to  on each side.

Find rate of change in area of the triangle .

Substitute corresponding values in the above expression.

square feet/sec.

Solution:

square feet/sec.