The area of the rectangle is increasing at a rate of 140 square centimeters per second.
Let's define the length as 'l' and the width as 'w'. The area of the rectangle is given by A = l * w. The rate of change of the area is represented by dA/dt.
Given:
dl/dt = 8 cm/s (rate of change of length)
dw/dt = 3 cm/s (rate of change of width)
l = 20 cm (initial length)
w = 10 cm (initial width)
To find the rate of change of area, we can use the product rule of differentiation:
dA/dt = l * dw/dt + w * dl/dt
Plugging in the known values:
dA/dt = 20 * 3 + 10 * 8 = 60 + 80 = 140 cm²/s
Therefore, the area of the rectangle is increasing at a rate of 140 square centimeters per second.
Question
The length of a rectangle is increasing at a rate of 8cm/s and its width is increasing at a rate of 3 cm/s. When the length is 20 cm and the width is 10 cm, how fast is the area of the rectangle increasing?