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SCALCET8 3.9.004.MI. The length of a rectangle is increasing at a rate of 7 cm/s and its width is increasing at a rate of 8 cm/s. When the length is 15 cm and the width is 7 cm, how fast is the area of the rectangle increasing

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Answer:

The area of the rectangle is increasing at a rate of 169 cm²/s

Step-by-step explanation:

Given;

increase in the length of the rectangle, [tex]\frac{dL}{dt} = 7 \ cm/s[/tex]

increase in the width of the rectangle, [tex]\frac{dW}{dt} = 8 \ cm/s[/tex]

length, L = 15 cm

width, W = 7 cm

The increase in Area is calculated as;

[tex]Area = Length \times Width\\\\A = LW\\\\\frac{dA}{dt} = L(\frac{dW}{dt} )\ + \ W(\frac{dL}{dt} )\\\\\frac{dA}{dt} = 15 \ cm(8\ \frac{ cm}{s} ) \ + \ 7 \ cm(7\ \frac{ cm}{s} ) \\\\\frac{dA}{dt} = 120 \ cm^2/s \ + \ 49 \ cm^2/s\\\\\frac{dA}{dt} = 169 \ cm^2/s[/tex]

Therefore, the area of the rectangle is increasing at a rate of 169 cm²/s

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