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Class 12 Tuition > Learn Applications of Derivatives > The length x of a rectangle is decreasing at the rate...
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The length x of a rectangle is decreasing at the rate of 3 cm/ mint and the width y is increasing at the rate of 2cm/min. when x = 10cm and y = 6cm, find the ratio of change of (a) the perimeter (b) the area of the rectangle

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Solution: Let length of rectangle =x cm and width of rectangle =y cm Given the length is decreasing at the rate of 3 cm/ minutes i.e. is decreasing w.r.t time dtdx=−3 cm/min.......(1) as x is decreasing and the width y is increasing at the rate of 2 cm/min i.e. y is increasing w.r.t...
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Solution: Let length of rectangle=xcm and width of rectangle=ycm Given the length is decreasing at the rate of3cm/ minutes i.e. is decreasing w.r.t time dtdx=−3cm/min.......(1)asxis decreasing and the widthyis increasing at the rate of2cm/min i.e.yis increasing w.r.t time dy/dt=2cm/min.........(2) (1) LetPbe the perimeter of rectangle =2(l+width) P=2(x+y) dp/dt=2,(dx/dt+dy/dt) Given :dx/dt=−3,dy/dt=2 ∴dp/dt=2(−3+2)=2×−1=−2cm/min ∴perimeter is decreasing at the rate of2cm/min (2) LetAbe the area of the rectangle A=l×width=xy⇒dA/dt=xdy/dt+ydtdx ⇒dA/dt=−3y+2xfrom(1)&(2) dA/dt∣∣∣∣x=10,y=6=−3×6+2×10=−18+20=2 Since are ismcm2dA/dt=2cm2/min Hence are is increasing at the rate of2cm2/min read less
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