Question

Question #65c39

Answer 1

The lengths of the sides have to be factors of `24`

`P = 2l+2b`

Explanation:

The area of a rectangle is found by multiplying the length by the breadth. `A = l xx b`

What are the factors of `24`?. Each of these could represent the length and breadth of a rectangle.

`24 = 24xx1" "rarr l = 24 and b =1`
`24 = 12xx 2" "rarr l=12 and b =2`
`24 = 8xx3" "rarr l = 8 and b = 3`
`24 = 6xx4" "larr l = 6 and b = 4`

We have four different rectangles with an area of `24` square units.

The perimeter is the sum of all the sides; `P = 2l + 2b`

`l = 24 and b =1" "rarrP = 48+2 = 50`
`l=12 and b =2" "rarrP = 24+4 =28`
`l = 8 and b = 3" "rarrP = 16+6 = 22`
`l = 6 and b = 4" "rarrP = 12+8 =20`

Notice that as the difference between the length and breadth decreases, the perimeter becomes smaller.

The smallest perimeter will be if the rectangle is a square where all the sides are equal.

`s= sqrt 24 = 4.89898`

`P = 4 xx sqrt24 = 19.60`