CPM Homework Help : AC Problem 10-126

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10-126.

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

tile $\space$	tile $\space$
tile $\space$	tile $\space$
tile $\space$	tile $\space$	tile $\space$

Figure 0

tile $\space$	tile $\space$	tile $\space$
tile $\space$	tile $\space$	tile $\space$
tile $\space$	tile $\space$	tile $\space$
tile $\space$	tile $\space$	tile $\space$	tile $\space$

Figure 1

tile $\space$	tile $\space$	tile $\space$	tile $\space$
tile $\space$	tile $\space$	tile $\space$	tile $\space$
tile $\space$	tile $\space$	tile $\space$	tile $\space$
tile $\space$	tile $\space$	tile $\space$	tile $\space$
tile $\space$	tile $\space$	tile $\space$	tile $\space$	tile $\space$

Figure 2

Hint:

The shapes are rectangles with one extra tile.
What is the formula for the area of a rectangle?

Answer:

One possible equation is
$(x+2)(x+3)+1=y$ , or
$x^2+5x+7=y$ .

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