The length l of a rectangle is decreasing at the rate of 3cm/sec, while its width w is increasing at the rate of 3cm/sec. Find the rates of change of (1.) the area, (2.) the perimeter, (3.) the length of one diagonal at the instant when l=15 and w=6.

Answer 1

a = xy
da/dt = y dx/dt + x dy/dt

d^2 = x^2+y^2

Now just plug in your numbers (I used x and y instead of w and l, since the l looks like a 1)

Answer 2

2. The length / of a rectangle is decreasing at the rate of 3 cm/sec,

while its width w is increasing at the rate of 3 cm/sec. Find the

rates of change of (a) the area, (b) the perimeter, (c) the length of

one diagonal at the instant when I = 15 and w = 6