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Home > CCA > Chapter 3 > Lesson 3.2.3 > Problem 3-58

3-58.

Examine the rectangles formed with tiles below. For each figure, write its area as a product of the width and length and as a sum of its parts.  

a.Positive algebra tiles connected in rows to form a large rectangle. First row: 1 horizontal X tile, and 1 unit tile. Second and third rows are the same as the first row. Fourth row: 1 X squared tile, and 1 vertical X tile.

  • Find the outside dimensions of the large rectangle.

    See dimensions below.

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

    As a product: multiply the dimensions of the large rectangle together.
    As a sum: add up the areas of all of the small rectangles.

    area as product (length)(width)
    area as sum

  1. Positive algebra tiles connected in rows to form a large rectangle. First row: 2 horizontal X tiles, and 1 unit tile. Second row is the same as the first row. Third row: 2 X squared tiles, and 1 vertical X tile.

  • Use the same method as part (a).

    Positive algebra tiles connected in rows to form a large rectangle. First row: 1 horizontal X tile and 4 unit tiles. Second row is the same as the first row. Third row: 1 X squared tiles and 4 vertical X tiles.

    area as a product  (length)(width)
    product as a sum 

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