Problema Solution
The length of a rectangle is increasing at a rate of 6cm/s and its width is increasing at a rate of 5cm/s. When the length is 20cm/s and the width is 15cm, how fast is the area of the rectangle increasing?
Answer provided by our tutors
Let
x = the length
y = the width
t = the time in seconds
The length of a rectangle is increasing at a rate of 6 cm/s means:
dx/dt = 6 cm/s
The width is increasing at a rate of 5 cm/s means:
dy/dt = 5 cm/s
The formula for the area of a rectangle is: A = xy
We need to find the change on the area per second: dA/dt
dA/dt = x(dy/dt) + y(dx/dt)
We plug the values that we have for dy/dt and dx/dt and x = 20 cm, y = 15 cm and get:
dA/dt = 20*5 + 15*6
dA/dt = 190 cm/s
The area of the rectangle is increasing at a rate of 190 cm^2/s.