The length of a rectangle is increasing at a rate of 6 centimeters per second and its width is increasing at a rate of 2 centimeters per second.

Question

The length of a rectangle is increasing at a rate of 6 centimeters per second and its width is increasing at a rate of 2 centimeters per second. When the length is 20 cm and the width is 10 centimeters, how fast is the area of the rectangle increasing?

Rate of change for area:---- square centimeters per second

Answer 1

Solution:

The area of a rectangle is A = LW where L is the length and W is the width

The rate of increasing length when L = 20 cm , dL/dt = 6 cm/s

The rate of increasing width when W = 10 cm , dW/dt = 2 cm/s

But dA/dt = d/dt( LW), dA/dt = L(dW/dt)+W(dL/dt) = 20cm(2cm/s)+10cm(6cm/s)

= 40cm²/s+60cm²/s = 100 cm²/s