calculus
posted by Janet .
The length of a rectangle is decreasing at the rate of 2 cm/sec, while the width w is increasing at the rate of 3 cm/sec. At what rate are the lengths of the diagonals changing at the instant that l=15 cm and w= 8 cm? Are the diagonals increasing or decreasing in length at this instant? Explain.
I worked through this but am not sure if I did it right or if I needed to work through as much as I did.
A=l*w
dA/dt=l*(dw/dt)+ w*(dl/dt = 4516= 29cm^2/sec
P=2l*2w =
2(dl/dt)+2(dw/dt)=4+6=2 cm/sec
Diagonal= (l^2+w^2)^1/2
dD/dt=(2l+2w)(.5)(l^2+w^2)^.5
=(30+16)(.5)(225+64)^.5
23/sqrt289=1.35 cm/sec
Did I need to do all this work, or just some of it or did I not even answer the orginally question?

Diagonal= (l^2+w^2)^1/2
then
dD/dt=(2 l dl/dt+2 w dw/dt)(.5)(l^2+w^2)^.5