Question

The width of a rectangle is increasing at a rate of 5 inches per second and its length is increasing at the rate of 9 inches per second. At what rate is the area of the rectangle increasing when its width is 2 inches and its length is 3 ​inches

Answer 1

Answer:

The area of rectangle is changing at the rate of 33 square inches per second.        

Step-by-step explanation:

We are given the following information:

Let W be the width of the rectangle and L be the length of rectangle.

Rate of change of width = $\frac{dW}{dt} = 5\text{ inches per second}$

Rate of change of length = $\frac{dL}{dt} = 9\text{ inches per second}$

We have to find rate of change of area at W = 2 and L = 3.

Rate of change of area = $\frac{dA}{dt}$

Area of rectangle = Length × Width

$\frac{dA}{dt} = \frac{d(LW)}{dt} = L\frac{dW}{dt} + W\frac{dL}{dt}$

Putting the values, we get

$\frac{dA}{dt} = 3(5) + 2(9) = 33\text{ square inches per second}$

The area of rectangle is changing at the rate of 33 square inches per second.