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?

5th square will be the first square to have a side length less than 12 inches

Step-by-step explanation:

The side of the first square = 24 inches

The side of the second square = 19.2

The ratio of the side of 1st square to the side of 2nd square = 19.2/24 = 4/5

The side of third square = 15.36 inches

The ratio of side of 2nd square to the side of 3rd square = 15.36/19.2 = 4/5

The side of the square is decreasing by the ratio = 4/5

The side of 4rth square = common ratio · side of third square

The side of 4rth square = 4/5 · 15.36 = 12.288 inches

The side of 5th square = common ratio · side of 4rth square

The side of 5th square = 4/5 · 12.288 = 9.8304 inches

Hence 5th square will be the first square to have a side length less than 12 inches