Orlando is making a design for a logo. he begins with a square measuring 20 inches on a side. the second square has a side length of 16 inches, and the third square has a side length of 12.8 inches. which square will be the first square with a side length of less than 8 inches?

The 6th square

Step-by-step explanation:

Let's find the answer by creating a number series and an equation for each side length reduction.

The data can be organize as:

20, 16, 12.8, ... which means that the side of the square has a length of 20 inches for the first one, 16 inches for the second one, 12.8 inches for the third one, etc.

The difference between the side length of squares 1 and 2 is:

20inches - 16inches = 4inches

The difference between the side length of squares 2 and 3 is:

16inches - 12.8inches = 3.2inches

Now, if you notice, the difference between 4inches and 3.2inches, which are how much the side length was reduced, can be calculated as a ratio, as follows:

3.2inches/4inches=0.8, which means that for the follow squares, the length is reduced to its 80% (0.8) of the previous reduction, which means that:

The first square start with a side length of 20 inches, but:

for the 2nd square de reduction was 4 inches (giving 20-4=16), then:

for the 3rd square we use the 80% reduction of the previous reduction: 0.8*4=3.2 (giving 16-3.2=12.8 inches)

for the 4th square we use the 80% reduction of the previous reduction: 0.8*3.2=2.56 (giving 12.8-2.56=10.24 inches)

for the 5th square we use the 80% reduction of the previous reduction: 0.8*2.56=2.048 (giving 10.24-2.048=8.192 inches)

for the 6th square we use the 80% reduction of the previous reduction: 0.8*2.048=1.6384 (giving 8.192-1.6384=6.5536 inches)

Notice how the last square (6th) has a side length less than 8 inches.

In conclusion, the 6th square will be the first square with a side length of less than 8 inches.

the answer is 489

step-by-step explanation: