Michael has 18 decorative square tiles to make a design on a kitchen backsplash. He wants to arrange them in a rectangular shape with the least perimeter possible. How many tiles will be in each row?
I think 18/3
To find the number of tiles in each row, we need to figure out the dimensions of the rectangular shape.
Let's assume that the number of tiles in each row is represented by 'x'. Hence, the number of rows will be represented by 'y'.
Since Michael has 18 tiles in total, we can write the equation:
x * y = 18
Now, we need to minimize the perimeter of the rectangular shape. The perimeter of a rectangle is given by the formula:
P = 2 * (length + width)
In this case, the length will be represented by 'x' and the width will be represented by 'y'.
So, the perimeter equation will be:
P = 2 * (x + y)
To minimize the perimeter, we can start with the assumption that the rectangle is a square, where x = y.
We can make a list of possible values for x and find the corresponding y values that satisfy the equation x * y = 18:
x = 1, y = 18
x = 2, y = 9
x = 3, y = 6
x = 6, y = 3
x = 9, y = 2
x = 18, y = 1
Out of these values, we see that when x = 3 and y = 6, the equation is satisfied.
Therefore, the rectangular shape will have 3 tiles in each row.