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Home > INT2 > Chapter 1 > Lesson 1.3.4 > Problem 1-114


Examine the rectangles formed with tiles below. For each figure, write an equation showing that its area as a product of the width and length is equal to its area as a sum of its parts.

  1. Find the outside dimensions of the large rectangle.

    See dimensions below.

    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. 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.

  1. Use the same method as part (a).