Question

The length of a rectangle is increasing at a rate of 5 cm/s and its width is increasing at a rate of 4 cm/s. When the length is 15 cm and the width is 6 cm, how fast is the area of the rectangle increasing?

Answer 1

The length of a rectangle is increasing at a rate of 5 cm/s i.e.

The width of the rectangle is increasing at a rate of 4 cm/s i.e.

If the width is 'w' and the length is 'l' then the area of rectangle is given by

Differentiating both sides w.r.t. time(t) ,we get

  

(Given: ; )

So, the rate of increase of the area of the rectangle is given by

When length, l is 15cm and the width, w is 6 cm the rate at which the area is increasing is given by

So, the area is increasing at a rate of 90 cm²/s.