Math, asked by sunilpnd8359, 2 months ago

The area of the rectangle below is 96 cm2. find x

Answers

Answered by amuthamary1979
0

Step-by-step explanation:

Let length and bredth of rectangle are x and y units respectively. Area =x×y.

x×y=96 => y= 96/x

P=2(l+b)

p=2(x+y)

p=2(x+96/x)=2x+192(1/x)

dp/dx=2–192/x^2. For minimum perimeter put dp/dx=0.

0=2–192/x^2

or 192/x^2=2

or 2x^2=192

or x^2=96

or x= 4.(6)^1/2 units

y=96/x=96/4.(6)^1/2= 4.(6)^1/2 unit

d2p^dx^2=2+384/x^3= + ve

There exist minima at x=4.(6)^1/2units.

In case minimum perimeter , each side of rectangle is 4.6^1/2 units i,e a square.

Minimum perimeter=2(4.6^1/2+4.6^1/2) units.

= 16.(6)^1/2 units. ,

Other - Cases:-

If , Area , x , y , p=2(x+y)

96=12×8 , 12 , 8 ,p=2(12+8)=40 units.

96=16×6 , 16 , 6 ,p=2(16+6)=44 units.

96=24×4 , 24 , 4 ,p=2(24+4)=56units

96=32×3 , 32 , 3 ,p=2(32+3)=70 units.

96=48×2 , 48 ,2 , p=2(48+2)=100 units.

96=96×1 , 96 , 1 , p=2(96+1)=194 units.

96=960×.1, 960 , .1, p=2(960+.1)=1920.2units

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