### Home > CCA > Chapter 9 > Lesson 9.1.4 > Problem 9-40

Find a rule that represents the number of tiles in Figure for the tile pattern below. Homework Help ✎

The red circles point out the left arms,

the green circles point out the rectangles,

and the blue circles point out the right arms.

Notice the following:

The length of the rectangle in Figure 1 is 3 units × 2 units;

the rectangle in Figure 2 is 4 units × 3 units;

and the rectangle in Figure 3 is 5 units × 4 units.

First, look at the left arm. It remains constant in each of these figures, with a value of

Let Figure number.

There is a rule for the size of the rectangles:

where

and

Now, consider the right arms. Its length matches its corresponding figure number.

left arm

Now simplify.