A rectangle has an area of 48 square yards. For what whole number values of length & width will the rectangle have the smallest perimeter?

6 and 8 6+6=12 8+8=16 12+16=28 perimeter also 6 x 8= 48 area

Ah, the elusive rectangle! Well, to find the smallest perimeter, we need to consider the factors of 48. So let's put on our mathematical clown shoes and get cracking!

The possible lengths and widths of the rectangle will be pairs of numbers whose product is 48. Let's take a look at a few options:

1) Length = 1 yard, Width = 48 yards: Perimeter = 1 + 48 + 1 + 48 = 98 yards.
2) Length = 2 yards, Width = 24 yards: Perimeter = 2 + 24 + 2 + 24 = 52 yards.
3) Length = 3 yards, Width = 16 yards: Perimeter = 3 + 16 + 3 + 16 = 38 yards.
4) Length = 4 yards, Width = 12 yards: Perimeter = 4 + 12 + 4 + 12 = 32 yards.
5) Length = 6 yards, Width = 8 yards: Perimeter = 6 + 8 + 6 + 8 = 28 yards.

Ta-da! The winner is option number 5, with a perimeter of 28 yards. So the rectangle with a length of 6 yards and a width of 8 yards will give us the smallest perimeter. Don't forget to bring your clown nose along when measuring!

To find the whole number values of length and width that will result in the rectangle having the smallest perimeter, we need to start by identifying the possible dimensions of the rectangle with an area of 48 square yards.

We know that the area of a rectangle is equal to its length multiplied by its width. In this case, the area is given as 48 square yards. We can represent this mathematically as:

length × width = 48

To find the whole number values of length and width, we can start by listing all the pairs of factors of 48. The factors of 48 are:

1 × 48
2 × 24
3 × 16
4 × 12
6 × 8

Now, we need to calculate the perimeter for each of these pairs of length and width values. The perimeter of a rectangle is the sum of all its sides, which in this case is:

perimeter = 2(length + width)

Let's calculate the perimeter for each pair:

1 × 48: perimeter = 2(1+48) = 2(49) = 98
2 × 24: perimeter = 2(2+24) = 2(26) = 52
3 × 16: perimeter = 2(3+16) = 2(19) = 38
4 × 12: perimeter = 2(4+12) = 2(16) = 32
6 × 8: perimeter = 2(6+8) = 2(14) = 28

From the calculations, we can see that the pair with the smallest perimeter is 6 × 8, which has a perimeter of 28.

Therefore, the whole number values for length and width that will result in the rectangle having the smallest perimeter are 6 and 8, respectively.