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?

The answer is fifth square.

Let's compare side lengths (a) of the first three squares:
1. square: a₁ = 24 inches
2. square: a₂ = 19.2 inches
3. square: a₃ = 15.36 inches



Therefore, everytime Orlando reduces side length 1.25 times.

Now, let's reduce side length of 3. square 1.25 to get side length of 4. square:
4. square: a₄ = ?

⇒ 
⇒
⇒ a₄ = 12.288 inches

Since 12.288 inches is still more than 12 inches, we need 5. square:
4. square: a₅ = ?

⇒ 
⇒
⇒ a₅ = 9.83 inches

Thus, fifth square is the first square with a side length (9.83 inches) of less than 12 inches.