A child has a large supply of dominoes, each of which measures 16 millimeters by 88 millimeters. She wants to lay them out to form a solid square, and she wants them all to be laid out horizontally. What will be the dimensions of the smallest square that she can form, and how many dominoes will it require?
To determine the dimensions of the smallest square and the number of dominoes required, we need to calculate the factors of both 16 mm and 88 mm.
Let's start with finding the factors of 16 mm:
The factors of 16 mm are: 1, 2, 4, 8, 16
Now, let's find the factors of 88 mm:
The factors of 88 mm are: 1, 2, 4, 8, 11, 22, 44, 88
Since the children want to lay the dominoes horizontally, we need to find a common factor of both 16 mm and 88 mm.
The common factors of 16 mm and 88 mm are: 1, 2, 4, 8
Now, we need to calculate the dimensions of the smallest square. To do this, we need to find the side length of the square that can be formed by using the common factors.
Since the dominoes are laid out horizontally, we need to use the longer side length, which is 88 mm.
The longest side of the square will be formed by arranging the dominoes along the perimeter of the square.
So, the side length of the square will be 88 mm.
Now, to calculate the number of dominoes required, we need to find out how many dominoes will fit along the side length of the square.
To do this, we divide the length of the side (88 mm) by the length of each domino (88 mm).
88 mm รท 88 mm = 1
Therefore, the square formed by laying the dominoes horizontally will have dimensions of 88 mm x 88 mm, and it will require 1 domino to complete the square.