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Home > AC > Chapter 8 > Lesson 8.3.3 > Problem 8-118

8-118.

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

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             Figure 1

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                Figure 2

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             Figure 3

The single unit tile is circled in red. The middle 2 by 3 rectangle is labeled in green. The one unit tile on the bottom right is circled in blue.

The single unit tile is circled in red. The middle 3 by 4 rectangle is labeled in green. The 2 unit tiles on the bottom right is circled in blue.

The single unit tile is circled in red. The middle 4 by 5 rectangle is labeled in green. The 3 unit tiles on the bottom right is circled in blue.

Figure 1

Figure 2

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 units units; the rectangle in Figure 2 is units units; and the rectangle in Figure 3 is units 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 represents the length and represents the width.

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

left arm rectangle right arm

Now simplify.