The length of a rectangle is increasing at a rate of 3 cm/s and its width is i

Question

The length of a rectangle is increasing at a rate of 3 cm/s and its width is increasing at a rate of 4 cm/s. When the length is 13 cm and the width is 6 cm, how fast is the area of the rectangle increasing?

Answer 1

A = L x W

Use the Product Rule to find the derivative of the area, dA/dt. The derivative is the rate that the area is increasing with time.

dA/dt = (dL/dt)W + L(dW/dt)

1. dA/dt = rate that the area of the rectangle is increasing
2. dL/dt = 3 cm/s
3. L = 13 cm
4. dW/dt = 4 cm/s
5. W = 6 cm

Plug in the numbers and compute the answer. The units are cm²/s.

Answer 2

Hello Kas,

The area of a rectangle is

A = L * W

→ (dA / dt) = L * (dW / dt) + W * (dL / dt), using Product Rule,

→ (dA / dt) = (13) * (4) + (6) * (3)

→ (dA / dt) = 52 + 18 = 70 cm²/sec.

Thank you for posting the question with Wyzant.

Kind regards,

Michael E.