### Home > CAAC > Chapter 8 > Lesson 8.3.3 > Problem 8-118

Find a rule that represents the number of tiles in Figure *x* 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 1.

Let *x* = Figure number.

There is a rule for the size of the rectangles:

(*x* + 2) (*x* + 1),

where (*x* + 2) represents the length

and (*x* + 1) represents the width.

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

*y* = left arm + rectangle + right arm*y* = 1 + (*x* + 2)(*x* + 1) + *x*

Now simplify.