1. A rectangle has a constant area of 200 square meters and its length L is increasing at the rate of 4 meters per second.

Question

a. Find the width W at the instant the width is decreasing at the rate of .4 meters per second.
b. At what rate is the diagonal D of the rectangle changing at the instant when the width W is 10 meters?

Answer 1

lw=200
l dw/dt+ W dl/dt=0
given dl/dt=4
a) find w then dw/dt=-.4
-.4*L+W*4=0
but remember LW=200 or L=200/W
-.4*200/W+4W=0
solve for W

b. diagonal D.

D= sqrt(L^2+W^2
dD/dt= 1/2 *1/sqrt( ) * (2L dl/dt+ 2W dw/dt)