Question

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

Answer 1

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