Section D Practice Problems

Problem 1

The perimeter of a rectangular park is 444 meters. The park is 175 meters long. How wide is the park? Explain or show your reasoning.

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Solution
47 meters. Sample response: First, I added 175 and 175 and that’s 350. I took 350 from 444 and that left 94. So, twice the other side length is 94. Since 2×47=942 \times 47 = 94, the other side length is 47 meters.

Problem 2

  1. Where do you see rhombuses in the design?
  2. Where do you see rectangles in the design?
  3. Are there any triangles in the design? Show your thinking. Organize it so it can be followed by others.

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Solution
Sample responses:
  1. In the middle there is a rhombus. And the white shapes in the center of the rectangles look like rhombuses.
  2. There are lots of rectangles going out from the middle in four directions.
  3. It is hard to tell. There are white shapes with three sides but it looks like one of the sides is curved in most of the shapes, so they wouldn’t be triangles.

Problem 3

Han is making a rectangular garden. He has 42 feet of fencing, and the garden needs to be at least 3 feet wide. What are the possible lengths and widths of the garden Han could make? Explain or show your reasoning.

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Solution
Sample response: One way to make 42 is 5+5+16+165 + 5 + 16 + 16. The garden could be 5 feet long and 16 feet wide or 16 feet wide and 5 feet long. Another way to make 42 is 10+10+11+1110 + 10 + 11 + 11. The garden could be 10 feet wide and 11 feet long or 10 feet long and 11 feet wide. Another way to make 42 is 2+2+19+192 + 2 + 19 + 19 but then the garden would not be wide enough.

Problem 4

The small square in this design is 6 inches long. What is the perimeter of the design? Explain or show your reasoning.

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Solution
204 inches. Sample response: I can see that two of the small squares are the same length as a big square. I also can see that two of the small squares are the same length as the long side of the rectangle. That means it takes 10 small squares to measure the long side of the big rectangle. Ten 6s is 60. It takes 7 small squares to measure the short side of the rectangle so that’s 42 inches. So, the perimeter is 60+42+60+4260 + 42 + 60 + 42 inches or 102+102102 + 102 inches, which is 204.