The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of 6 cm/s. when the length is 13 cm and the width is 5 cm, how fast is the area of the rectangle increasing?

Given :

The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of 6 cm/s.

When the length is 13 cm and the width is 5 cm .

To find :-

how fast is the area of the rectangle increasing?

Solution :-

As we know that :-

A = lb

To find the rate :-

d(A)/dt = d(lb)/dt .

Differenciate :-

dA/dt = l (db/dt ) + b (dl/dt )

Substitute :-

dA/dt = 13*7 + 5* 8

dA/dt = 91 + 40 cm²/s

dA/dt = 131 cm²/s