Question

3. The length of a rectangle is increasing at a rate of 3 cm=s and its width is increasing at arate of 9 cm=s. When the length is 7 cm and the width is 5 cm, how fast is the area of therectangle increasing?

Answer 1

Answer:

$\frac{dA}{dt} = 78cm/sec$

The area of the rectangle is increasing at 78cm/sec

Step-by-step explanation:

Explanation:-

Given the length of a rectangle is increasing at a rate of 3 cm/s

$\frac{dl}{dt} = 3cm/s$

Given the width of a rectangle is increasing at a rate of 9 cm/s

$\frac{dw}{dt} = 9cm/s$

we know that the area of the rectangle

                         A = l × w  …(l)

Differentiating equation with respective to 't'

$\frac{dA}{dt} = l (\frac{dw}{dt} )+ w (\frac{dl}{dt} )$

Given the length of the rectangle = 7 cm and

The width of the rectangle w = 5 cm

$\frac{dA}{dt} = 7(9)+5(3) = 78$

$\frac{dA}{dt} = 78cm/sec$

Final answer:-

The area of the rectangle is increasing at 78cm/sec