The length of a rectangle is increasing at a rate of 9 cm/s and its width is increasing at a rate of 7 cm/s. When the length is 11 cm and the width is 7 cm, how fast is the area of the rectangle increasing?

dA/dt = 140  cm²/s

Explanation:

The length of a rectangle is increasing at the rate of 9 cm/s . This means rate at which the length is changing with time  = 9 cm/s

dL/dt = 9 cm/s

The width is increasing at the rate of 7 cm/s.  

dW/dt = 7 cm/s

When the length is 11 cm and the width is 7 cm, How fast is the area of the rectangle increasing?

Area of a rectangle = Length × width

Area of a rectangle = Lw

we need the product rule to find the rate the area of the rectangle is changing.

dA/dt = LdW/dt  + W dL/dt

dA/dt = 11 (7) + 7(9)

dA/dt = 77 + 63

dA/dt = 140  cm²/s