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Alex and Maria were trying to find the side labeled in problem 6-92. Their work is shown below.  

Alex:I noticed that when I multiplied by , the sides of the triangle got longer.

Maria:I remember that when we were dilating shapes in Lesson 6.2.2, my shape got bigger when I divided by .

  1. Look at each student’s work. Why do both multiplying by and dividing by make the triangles larger?

    Since we know that multiplication and division are opposite operations, how can we explain why this happens?

    Consider what happens when you multiply a shape by a number less than ; the shape becomes smaller.
    On the other hand, dividing by a number larger than will also cause a shape to become smaller.
    Are the two expressions above any different?

  2. Use Alex and Maria’s strategy to write two expressions to find the value of in problem 6-92.

    Try using the same factors as Alex and Maria to multiply or divide by the appropriate side length to find the value of . Refer to Problem 6-94 for help.

    Use the side length as the multiple or divisor.