Question

The length of the rectangle is changing at a rate of 4 cm/s and the area is changing at the rate of 8 cm/s. What will be the rate of change of width if the length is 4cm and the width is 1 cm.

(a) 5 cm/s

(b) 6 cm/s

(c) 2 cm/s

(d) 1 cm/s

The question was asked in an online quiz.

Question is from Derivatives Application in chapter Application of Derivatives of Mathematics – Class 12

Answer 1

The correct choice is (d) 1 cm/s

The explanation is: Let the length be l, width be b and the area be A.

The Area is given by A=lb

\(\frac{dA}{dt}\)=l.\(\frac{db}{dt}\)+b.\(\frac{dl}{dt}\) -(1)

Given that, \(\frac{dl}{dt}\)=4cm/s and \(\frac{dA}{dt}\)=8 cm/s

Substituting in the above equation, we get

8=l.\(\frac{db}{dt}\)+4b

Given that, l=4 cm and b=1 cm

∴8=4(\(\frac{db}{dt}\))+4(1)

8=4(\(\frac{db}{dt}\))+4

\(\frac{db}{dt}\)=1 cm/s.