### Home > INT2 > Chapter 7 > Lesson 7.1.1 > Problem 7-13

Write an equation that represents the number of tiles in Figure for the tile pattern below.

tile | tile | tile | |

tile | tile | ||

tile | tile | tile |

Figure 1

tile | tile | tile | tile | ||

tile | tile | tile | |||

tile | tile | tile | |||

tile | tile | tile | tile | tile |

Figure 2

tile | tile | tile | tile | tile | |||

tile | tile | tile | tile | ||||

tile | tile | tile | tile | ||||

tile | tile | tile | tile | ||||

tile | tile | tile | tile | tile | tile | tile |

Figure 3

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

the rectangle in Figure 2 is

and the rectangle in Figure 3 is

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 arm. Its length matches its corresponding figure number.

left arm

Now simplify.