What are the dimensions of the smallest square that you can make using 18-in. by 24-in. rectangular tiles?
A. 36-in. by 36-in.
B. 144-in. by 144-in.
C. 60-in. by 60-in.
D. 72-in. by 72-in.
This is like finding the LCM for 18 and 24 which would be 72
so the smallest square is 72 by 72
you would need 12 tiles, laid out in 3 rows and 4 columns, each row 24 inches and each column 18 inches
Thanks so much!!! I never understood how to do this, now I do :)
Well, let me clown around with the dimensions for a moment. If we try to make a square with 18-in. by 24-in. tiles, we have to see if they fit evenly. Now, the only way that's gonna happen is if the tiles can unite without any leftovers.
To find the dimensions of the square, we need to find the greatest common divisor (GCD) of 18 and 24. The GCD of 18 and 24 is 6. So, we can divide both 18 and 24 by 6, giving us a square with dimensions of 3-in. by 4-in.
However, none of the answer choices provided match these dimensions, so it seems whoever came up with those options didn't give us a choice that perfectly fits the tiles. Therefore, we can conclude this question doesn't have a fitting answer. It's a "square deal" breaker, I guess!
To find the dimensions of the smallest square that can be made using the given rectangular tiles, we need to determine the greatest common divisor (GCD) of the tile dimensions.
The GCD of 18 and 24 can be found by listing the factors of each number and identifying the largest number that divides both:
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
From this list, we can see that the largest number that divides both 18 and 24 is 6. Therefore, the GCD of 18 and 24 is 6.
Since a square has equal sides, we can divide both the length and width of the given rectangular tiles by the GCD (6) to determine the dimensions of the smallest square.
Dividing 18 by 6 gives us 3, and dividing 24 by 6 gives us 4. Therefore, the dimensions of the smallest square that can be made using the 18-in. by 24-in. rectangular tiles are 3-in. by 4-in.
However, none of the given answer choices match these dimensions.
To find the dimensions of the smallest square that can be made using 18-in. by 24-in. rectangular tiles, we need to determine the greatest common divisor (GCD) of 18 and 24.
The GCD is a number that divides both 18 and 24 without leaving a remainder.
To find the GCD, we can use the Euclidean algorithm:
1. Divide 24 by 18: 24 ÷ 18 = 1 with a remainder of 6.
2. Divide 18 by 6: 18 ÷ 6 = 3 with no remainder.
3. Since there is no remainder, 6 is the GCD of 18 and 24.
Now that we have the GCD, we can use it to find the dimensions of the smallest square.
The GCD of 18 and 24 is 6, so we can divide both sides by 6 to simplify:
18 ÷ 6 = 3 and 24 ÷ 6 = 4.
Therefore, each tile is a 3-in. by 4-in. rectangle.
To form a square, we need to find the side length of the square by taking the GCD of 3 and 4.
The GCD of 3 and 4 is 1.
Therefore, the side length of the square made with these tiles is 1 inch.
Now, let's check the answer choices:
A. 36-in. by 36-in.: Each side of this square is 36 inches, which is not the smallest square that can be made.
B. 144-in. by 144-in.: Each side of this square is 144 inches, which is not the smallest square that can be made.
C. 60-in. by 60-in.: Each side of this square is 60 inches, which is not the smallest square that can be made.
D. 72-in. by 72-in.: Each side of this square is 72 inches, which is not the smallest square that can be made.
None of the answer choices is correct.
The correct answer is that the dimensions of the smallest square that can be made using 18-in. by 24-in. rectangular tiles is 1-inch by 1-inch.