Question

Calculus Rate of Change help

Answer 1

The length L of a rectangle is decreasing at the rate of 2cm/sec while the width W is increasing at the rate of 2cm/sec. when l=12 cm and w=5cm, find the rates of change of a) the area, b) the perimeter, c) the length of a diagonal of the rectangle

Answer 2

I already did a and I got da/dt= -14 cm^2/sec

Answer 3

perimeter=2l+2w
24+10=34
dl=-2
dw=5
2dl+2dw=2(-2)+2(2)
-4+4cm/sec

Answer 4

ohh so the perimeter doesn't change

Answer 5

Now for part c, do I use the Pythagorean Theorem?

Answer 6

yes

Answer 7

Ok so I have dc/dt=1/2(L^2+W^2)*2L*dL/dt + 2W*dW/dt

Answer 8

http://mathhelpforum.com/calculus/20050-related-rates.html

Answer 9

Find the rate of change of the diagonals.

Let D = a diagonal of the w by L rectangle,
By Pythagorean theorem,
D^2 = w^2 +L^2
So,
D = sqrt[w^2 +L^2]
Or,
D = [w^2 +L^2]^(1/2)

Answer 10

ok after taking the deriv i get dc/dt=1/2(L^2+W^2)*2L*dL/dt + 2W*dW/dt