Question

The area of a rectangle whose length is twice its width, is increasing at the rate of 8 cm.find the rate at which the length is increasing when the width is 5 cm

Answer 1

Answer:

140

cm

2

/

s

Explanation:

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