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A rectangle with an area of 96 square centimeters has whole number side lengths. What is the difference between the greatest and least perimeter of the rectangles

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Answer:

154 cm

Explanation:

We are given that

Area of rectangle=A=96 square cm

We have to find the difference between the greatest and least perimeter of the rectangles.

Let

Length of rectangle,l=x

Breadth of rectangle.b=y

Area of rectangle=
l* b=xy


xy=96

Factors of 96 are

1,2,3,4,6,8,12,16,24,32,48,96


96* 1=96


48* 2=96


32* 3=96


24* 4=96


16* 6=96


12* 8=96

Perimeter of rectangle,P=
2(x+y)

When x=96 an y=1

P=
2(96+1)=194 cm

When x=48 and y=2


P=2(48+2)=100 cm

When x=24 and y=4


P=2(24+4)=56 cm

When x=16 and y=6


P=2(16+6)=44 cm

When x=12 and y=8


P=2(12+8)=40 cm

When x=32 and y=3


P=2(32+3)=70 cm

Greatest perimeter of rectangle=194 cm

Least perimeter of rectangle=40 cm

Difference between the greatest and least perimeter of the rectangles=194-40=154 cm

User EKrueger
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