The length of a rectangle is increasing by 7 cm/s and its width is increasing at a rate of 9 cm/s. When the length is 15 cm and the width is 7 cm, how fast is the area of the rectangle increasing?

Question

please help as soon as possible

Answer 1

Given: l = 15 cm, w = 7 cm, dl/dt = 7 cm/s, dw/dt = 9 cm/s

Answer: The area of a rectangle is given by: A = w * l, if we differentiate both sides with respect to time, we end up with dA/dt = d/dt(w * l). To differentiate (w * l), we need to use the product rule with implicit differentiation. Thus we get:

dA/dt = w*dl/dt + l * dw/dt

Plugging in our given numbers, we find dA/dt = (7cm * 7cm/s) + (15cm * 9cm/s) = 184 cm/s

Answer 2

isn't it

Area(t)=l(t)*w(t)

dA/dt=l(t)*w'(t)+l'(t)w(t)

at some t, l(t)=15,w'(t)=9,l'(t)=7, w(t)=7

at that t

dA/dt=15*9+7*7