To minimize the perimeter of a rectangle formed by 12 square tiles, we need to find the factors of 12 and check which combination results in the smallest perimeter.
The factors of 12 are 1, 2, 3, 4, 6, and 12. We can form a rectangle with each of these factors, by finding the corresponding quotient of 12 divided by the factor. For example, if we use a factor of 2, we can arrange the 12 tiles in a rectangle with dimensions 2 x 6 or 6 x 2.
The perimeter of a rectangle is given by the formula P = 2L + 2W, where L is the length and W is the width. For each possible combination of dimensions, we can calculate the corresponding perimeter:
For a rectangle with dimensions 1 x 12, the perimeter is P = 2(1) + 2(12) = 26.
For a rectangle with dimensions 2 x 6, the perimeter is P = 2(2) + 2(6) = 16.
For a rectangle with dimensions 3 x 4, the perimeter is P = 2(3) + 2(4) = 14.
For a rectangle with dimensions 4 x 3, the perimeter is P = 2(4) + 2(3) = 14.
For a rectangle with dimensions 6 x 2, the perimeter is P = 2(6) + 2(2) = 16.
For a rectangle with dimensions 12 x 1, the perimeter is P = 2(12) + 2(1) = 26.
Therefore, we can see that the combination of dimensions that results in the smallest perimeter is a rectangle with dimensions 3 x 4, and there will be 3 tiles in each row