Question

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

one diagonal at the instant when l = 15 and w = 6.

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

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

Answer 1

for ease of reading, I'll use x and y for length and width
Hmmm. It appears you meant to say

The length l 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.

the diagonal
d^2 = x^2 + y^2
so at the given moment,
d = 3√29
area a = 90

area a = xy
da/dt = y dx/dt + x dy/dt
= 6(-3) + 15(3) = 27 cm^2/s

see what you can do with the perimeter
I have no idea what the (c) part is

It's <u>not my job</u> to figure out what you mean.
It's your job to say it so clearly you cannot be misunderstood.