Alex wants to decorate her bedroom wall with colored square paper. She wants all the squares to be the same size to make a checkerboard design. The area to tile is a rectangle measuring 80 inches by 96 inches. The paper squares come in widths of 10in, 12in, 16in and 20in.
Which size tile do you recommend Alex buys? Explain or show your reasoning for this choice.
the 80 and 96 inches should both be a whole number multiple of the paper square size
only one size works
To determine the best tile size for Alex's bedroom wall, we need to consider the dimensions of the wall and the available tile sizes.
The wall dimensions are 80 inches by 96 inches, which means we need to find the greatest common divisor (GCD) of these two numbers. The GCD will give us the size of the largest possible square that evenly divides both the length and width of the wall.
In this case, the GCD of 80 inches and 96 inches is 16 inches. This means that we can evenly divide the wall into squares of size 16 inches by 16 inches.
Now let's consider the available tile sizes: 10 inches, 12 inches, 16 inches, and 20 inches. Since the GCD of the wall dimensions is 16 inches, it makes sense to choose tiles with a size that can evenly divide into 16 inches.
Out of the available options, the only tile size that can evenly divide 16 is 16 inches itself. This means that Alex should buy tiles with a size of 16 inches.
By using tiles with a size of 16 inches, Alex will be able to perfectly cover the entire wall without having to cut any tiles. This will create a checkerboard design with squares of equal size.