Step 1:

Let the 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.

Differentiate with respect to  on each side.

Find value at  feet .

Step 2:

Substitute corresponding values in above expression to find  .

Area of the triangle .

Differentiate with respect to  on each side.

Here we need to find rate of change of area of the triangle at feet ,that is .

substitute corresponding values in the above expression.

square feet/sec.

Solution:

square feet/sec.