Question

the length and breadth of a rectangular are 2×2 – 2y + 5 and -4×2 + 8y-2. find the perimeter of the rectangle. what will be the perimeter of rectangle if x = 1 and y = 2 ?​

Answer 1

Answer:

It is given that length (x) is decreasing at the rate of 5 cm/min

and the width (y) is increasing at the rate of 4 cm/min,

⇒dtdx=−5 cm/min and dtdy=4  cm/min

Thus the perimeter (P) of a rectangle is, P=2(x+y)

dtdP=2(dtdx+dtdy)=2(−5+4)=−2 cm/min

Hence, the perimeter is decreasing at the rate of 2 cm/min.

(ii)

It is given that length (x) is decreasing at the rate of 5 cm/min 

and the width (y) is increasing at the rate of 4 cm/min, 

⇒dtdx=−5 cm/min and dtdy=4  cm/min

Thus the area (A) of a rectangle is, A=xy

∴(dtdA)x=8,y=6=(ydtdx+xdtdy)x=8,y=6=6(−5)+8(4)=2 cm2/min

Step-by-step explanation:

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