# Math Help - Related Rates: Changing Dimensions in a Rectangle

1. ## Related Rates: Changing Dimensions in a Rectangle

I am so confused on this one. I don't know if I'm suppose to use implicit differentiation like my other problems or what.

Problem: 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. While L= 12 cm and W= 5 cm, find the rates of change of
a) the area
b) the perimeter
c) the length of a diagonal in the rectangle

2. Originally Posted by LShimabukuro
I am so confused on this one. I don't know if I'm suppose to use implicit differentiation like my other problems or what.

Problem: 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. While L= 12 cm and W= 5 cm, find the rates of change of
a) the area
b) the perimeter
c) the length of a diagonal in the rectangle
a) $A = LW \Rightarrow \frac{dA}{dt} = L \frac{dW}{dt} + W \frac{dL}{dt}$ using the product rule. Therefore $\frac{dA}{dt} = (12) (2) + (5) (-2) = ....$

b) $P = 2W + 2L \Rightarrow \frac{dP}{dt} = ....$

c) $D = \sqrt{L^2 + W^2} \Rightarrow \frac{dD}{dt} = \frac{1}{2 \sqrt{L^2 + W^2}} \cdot \left(2L \frac{dL}{dt} + 2W \frac{dW}{dt} \right)$ using the chain rule. Therefore ....