Answer:
154 cm
Step-by-step 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=[tex]l\times b=xy[/tex]
[tex]xy=96[/tex]
Factors of 96 are
1,2,3,4,6,8,12,16,24,32,48,96
[tex]96\times 1=96[/tex]
[tex]48\times 2=96[/tex]
[tex]32\times 3=96[/tex]
[tex]24\times 4=96[/tex]
[tex]16\times 6=96[/tex]
[tex]12\times 8=96[/tex]
Perimeter of rectangle,P=[tex]2(x+y)[/tex]
When x=96 an y=1
P=[tex]2(96+1)=194 cm[/tex]
When x=48 and y=2
[tex]P=2(48+2)=100 cm[/tex]
When x=24 and y=4
[tex]P=2(24+4)=56 cm[/tex]
When x=16 and y=6
[tex]P=2(16+6)=44 cm[/tex]
When x=12 and y=8
[tex]P=2(12+8)=40 cm[/tex]
When x=32 and y=3
[tex]P=2(32+3)=70 cm[/tex]
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
