Answer:
The area of a rectangle is given by the formula A = L x W where A is the area, L is the length, and W is the width.
To find how fast the area of the rectangle is increasing, we need to differentiate the formula for A with respect to time t:
dA/dt = d/dt(L x W)
Using the product rule of differentiation, we get:
dA/dt = dL/dt x W + L x dW/dt
Given that dL/dt = 5 cm/s, dW/dt = 4 cm/s, L = 9 cm, and W = 6 cm, we can substitute these values in the above formula to get the rate at which the area of the rectangle is increasing:
dA/dt = (5 cm/s) x (6 cm) + (9 cm) x (4 cm/s)
dA/dt = 30 cm^2/s + 36 cm^2/s
dA/dt = 66 cm^2/s
Therefore, the area of the rectangle is increasing at a rate of 66 cm^2/s when the length is 9 cm and the width is 6 cm.