Orlando is making a design for a logo. He begins with a square measuring 22 inches on a side.

The second square has a side length of 17.6 inches, and the third square has a side length of

14.08 inches. Which square will be the first square with a side length of less than 10 inches?

A) fifth square

B) fourth square

C) sixth square

D) seventh square

the answer is A i had a quiz

Answer: A

Step-by-step explanation:

The first square is 22 inches on a side.

The second is 17.6 inches on a side

the third is 14.08 inches on a side.

We can suppose that we have a constant rate of decrease betwen the sides cubes, this means that:

22in*x = 17.6in

where x is the rate of scale.

x = 17.6/22 = 0.8

Now we test this with the second and third:

17.6in*0.8 = 14.08in

Ok, this works.

then the side of n-th cube can be found with the equation

L = 22*0.8^ (n-1)

we can try the different options and see which one gives a value smaller than 10.

A) n = 5

L = 22*0.8^4 = 9.01

Then the correct option is A