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The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of 6 cm/s. When the length is 7 cm and the width is 4 cm, how fast is the area of the rectangle increasing?

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Given :

  • The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of 6 cm/s.
  • When the length is 7 cm and the width is 4 cm .

To find :-

  • how fast is the area of the rectangle increasing?

Solution :-

As we know that :-

  • A = lb

To find the rate :-

  • d(A)/dt = d(lb)/dt .

Differenciate :-

  • dA/dt = l (db/dt ) + b (dl/dt )

Substitute :-

  • dA/dt = 6*7 + 4* 8
  • dA/dt = 42 + 32 cm²/s
  • dA/dt = 74 cm²/s

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