Question

The length of a rectangle is increasing at the rate of 8 cm/s and its width is increasing at the rate of 5 cm/s. when the length is 20 cm and the width is 12 cm, how fast is the area of the rectangle increasing at that instant?

Answer 1

The rate at which the area of the rectangle is increasing at that instant is 196 cm²/s.

Step-by-step explanation:

To find the rate at which the area of the rectangle is increasing, we can use the formula for the area of a rectangle, which is length multiplied by width. Let's denote the length as L and the width as W, and the rate at which the length is increasing as dL/dt and the rate at which the width is increasing as dW/dt.

Given that dL/dt = 8 cm/s and dW/dt = 5 cm/s, we need to find dA/dt, which represents the rate at which the area is increasing. Since A = L * W, we can use the product rule of differentiation to find dA/dt.

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

Now, substitute the given values of dL/dt = 8 cm/s, dW/dt = 5 cm/s, L = 20 cm, and W = 12 cm into the equation to find dA/dt.

dA/dt = 12 cm * 8 cm/s + 20 cm * 5 cm/s = 96 cm²/s + 100 cm²/s = 196 cm²/s.