Orlando is making a design for a logo. He begins with a square measuring 24 inches on a side. The second square has a side length of 19.2 inches, and the third square has a side length of 15.36 inches. Which square will be the first square with a side length of less than 12 inches?
Orlando is dividing the side length of the previous square by 1.25 each time. We can use this pattern to find the side length of the square after the third square:
15.36 ÷ 1.25 = 12.288
Therefore, the fourth square will have a side length of 12.288 inches, which is the first square with a side length less than 12 inches.
are you sure
Yes, I'm sure.
The side lengths of the first three squares are:
- Square 1: 24 inches
- Square 2: 24 ÷ 1.25 = 19.2 inches
- Square 3: 19.2 ÷ 1.25 = 15.36 inches
To find the side length of the fourth square, we divide the side length of the third square by 1.25:
- Square 4: 15.36 ÷ 1.25 = 12.288 inches
Therefore, the side length of the fourth square is 12.288 inches, which is the first square with a side length less than 12 inches.
how is 12.288 inches less than 12 inches
You are right, I apologize for my mistake. I made an error in my calculations.
To find the first square with a side length of less than 12 inches, we need to continue dividing the side length of the previous square by 1.25 until we get a length less than 12 inches. We can write this as:
24 ÷ 1.25^x < 12
Where x is the number of times we divide by 1.25. To solve for x, we can take the logarithm of both sides:
log(24) - x log(1.25) < log(12)
x log(1.25) > log(24) - log(12)
x > (log(24) - log(12)) / log(1.25)
x > 2.176
Since x has to be a whole number, the first square with a side length less than 12 inches will be the fifth square. We can find its side length by dividing the side length of the fourth square by 1.25:
15.36 ÷ 1.25 = 12.288 inches
And then dividing by 1.25 again:
12.288 ÷ 1.25 = 9.8304 inches
Therefore, the side length of the fifth square is 9.8304 inches, which is the first square with a side length less than 12 inches. I'm sorry for any confusion my previous answer might have caused.
yeah please be more thorough
Certainly! To find the first square with a side length of less than 12 inches, we need to continue dividing by 1.25 until we obtain a length less than 12 inches. We can start by dividing the side length of the first square by 1.25 repeatedly, until we find the square that has a side of less than 12 inches.
The side lengths of the first four squares are:
- Square 1: 24 inches
- Square 2: 24 ÷ 1.25 = 19.2 inches
- Square 3: 19.2 ÷ 1.25 = 15.36 inches
- Square 4: 15.36 ÷ 1.25 = 12.288 inches
We see that the side length of the fourth square is 12.288 inches, which is not less than 12 inches. To find the fifth square, we need to continue dividing:
- Square 5: 12.288 ÷ 1.25 = 9.8304 inches
Now, the side length of the fifth square is 9.8304 inches, which is less than 12 inches. So the answer to the question is that the fifth square will be the first square with a side length of less than 12 inches.