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