CPM Homework Help : CCA Problem 3-49

Write the area of the rectangle at right as a product and as a sum.

Positive algebra tiles connected in rows to form a large rectangle. First row: 2 horizontal X tiles, and 4 unit tiles. Second row is the same as the first row. Third row is 2 X squared tiles, and 4 vertical X tiles.

Step 1:

Find the height and the base by finding the dimensions of each row and column.

Labels added: The left side of the large rectangle is labeled height and the bottom side is labeled base.

Hint 1:

Labels added: On the left edge of the rectangle, the left sides of the tiles are labeled, 1, 1, and X. On the bottom edge of the rectangle, the bottom sides of the tiles are labeled, X, X, 1, 1, 1, 1.

$\text{height}=x+2\ \ \ \ \ \ \ \ \ \ \text{base}=2x+4$

Step 2:

To find the area as a product, $\text{area} = \text{base} × \text{height}$ .

Hint 2:

$\text{area} = (2x + 4)(x + 2)$

Step 3:

To express the area as a sum, add up all of the tiles and simplify.

Hint 3:

$x + x + 1 + 1 + 1 + 1 + x + x + 1 + 1 + 1 + 1 + \\x² + x² + x + x + x + x = 2x² + 8x + 8$

Answer:

$\text{Area as a product}=(2x+4)(x+2)$
$\text{Area as a sum} = 2x² + 8x + 8$