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.