Answered

Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Join our platform to get reliable answers to your questions from a knowledgeable community of experts. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

The length of a rectangle is increasing at a rate of 4 cm/s and its width is increasing at a rate of 4 cm/s. When the length is 5 cm and the width is 4 cm, how fast is the area of the rectangle increasing

Sagot :

21700137

Let us set up the following variables:

⎧

⎪

⎪

⎪

⎪

⎨

⎪

⎪

⎪

⎪

⎩

l

Length of Rectangle (cm)

w

Width of Rectangle (cm)

A

Area of Rectangle (

c

m

2

)

t

Time (s)

We are told that:

d

l

d

t

=

8

cm/s (const), and,

d

w

d

t

=

3

cm/s (const)

The Area of the rectangle is:

A

=

l

w

Differentiating wrt

t

(using the product rule) we get;

d

A

d

t

=

(

l

)

(

d

w

d

t

)

+

(

d

l

d

t

)

(

w

)

∴

d

A

d

t

=

3

l

+

8

w

So when

l

=

20

and

w

=

10

⇒

d

A

d

t

=

3

⋅

20

+

8

⋅

10

∴

d

A

d

t

=

60

+

80

∴

d

A

d

t

=

140

cm

2

/

s

We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.