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Lyrx [107]
3 years ago
15

The width of a rectangle is increasing at a rate of 2 cm/sec, while the length increases at 3 cm/sec. At what rate is the area i

ncreasing when w = 4cm and l = 5cm?
Mathematics
1 answer:
lorasvet [3.4K]3 years ago
4 0

Answer:

The area of the rectangle is increasing at a rate of  22\ cm^2/s.

Step-by-step explanation:

Given : The width of a rectangle is increasing at a rate of 2 cm/ sec. While the length increases at 3 cm/sec.

To find : At what rate is the area increasing when w = 4 cm and I = 5 cm?

Solution :

The area of the rectangle with length 'l' and width 'w' is given by  A=l w

Derivative w.r.t  't',

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

Now, we have given

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

l=5\ cm

\frac{dw}{dt}=2\ cm/s

w=4\ cm

Substitute all the values,

\frac{dA}{dt}=(4)(3)+(5)(2)

\frac{dA}{dt}=12+10

\frac{dA}{dt}=22\ cm^2/s

Therefore, the area of the rectangle is increasing at a rate of  22\ cm^2/s.

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