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 the perimeter, and the length of one diagonal at the instant when l=15 and w=6.

Answer 1

given : dl/dt = 3 cm/s, dw/dt 3 cm/s

P = 2l + 2w
dP/dt = 2 dl/dt + 2 dw/dt
plug in the values

d^2 = l^2 + w^2

I assume you want the rate of change of the perimeter, not just its length. Your wording is confusing.

2d dd/dt = 2l dl/dt + 2w dw/dt
you are given l and w, so you can find d.
plug in the values to find dd/dt