Length of a rectangle is increasing at a rate of  cm/sec.

Width of the rectangle is increasing at a rate of  cm/sec .

Therefore,  cm/sec and  cm/sec.

Length of the rectangle is  cm and width of the rectangle is  cm.

Area of a rectangle is  .

Rate of change of area is  .

.

Product rule of derivative is .

.

Substitute corresponding values in above expression. 

Rate of change of area  cm²/sec.

Area of the rectangle is increasing at a rate of  cm²/sec.