Mrs. Smith has 42 carpet squares. How should she arrange them so that she has the smallest perimeter?
To arrange the carpet squares in order to obtain the smallest perimeter, Mrs. Smith should arrange them in the shape of a square. This will reduce the amount of edging needed, resulting in the smallest perimeter possible.
To determine the length of each side of the square, we can divide the total number of carpet squares, which is 42, by 4 (since a square has 4 equal sides).
42 divided by 4 equals 10.5, so each side of the square should have a length of 10.5 carpet squares.
However, since each side needs to be a whole number, we can round down the length to 10 carpet squares per side.
Therefore, Mrs. Smith should arrange her 42 carpet squares in the form of a square with 10 carpet squares per side. This arrangement will yield the smallest perimeter.
To find the arrangement that gives the smallest perimeter, Mrs. Smith should arrange the carpet squares in a square-shaped pattern. In a square, all sides are equal in length, which results in the smallest perimeter.
To calculate the side length of the square, we can find the square root of the total number of carpet squares (42). The square root of 42 is approximately 6.48. However, since we cannot have a fraction of a carpet square, we need to round this value to the nearest whole number. Therefore, Mrs. Smith should arrange the carpet squares in a square with side length 6.
By arranging the 42 carpet squares in a 6 by 7 pattern (6 rows and 7 columns), Mrs. Smith will create a square with the smallest perimeter. Each side of the square will have a length of 6 carpet squares, resulting in a total perimeter of 6 + 6 + 7 + 7 = 26 carpet squares.
I think they are supposed to form a solid area of carpet.
A square has the smallest perimeter, so we shpuld try to get as close to that as possible.
6x7 has a perimeter of 26
If Mrs. Smith wants the smallest perimeter out of her 42 carpet squares, she should arrange them in a square with each side having 10 carpet squares and the remaining two laid across the middle.
This will make a square-shaped area of 10 by 10 carpet squares, which will have a perimeter of 40 carpet squares. The two remaining carpet squares can be laid on top of each other in the middle of the square, so they won't affect the perimeter.
Any other arrangement will have a larger perimeter, since the distance around the edge of the square will be shorter than any other shape that can be made with 42 carpet squares.