Question

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 7 cm and the width is 4 cm, how fast is the area of the rectangle increasing?

Answer 1

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 7 cm and the width is 4 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 = 6*7 + 4* 8
• dA/dt = 42 + 32 cm²/s
• dA/dt = 74 cm²/s