Section C Practice Problems

Problem 1

A rectangular card has an area of 60 square centimeters. It is 4 centimeters longer than it is wide. What is the perimeter of the card? Explain or show your reasoning.

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Solution
32 centimeters. Sample response: Since the area is 60 square centimeters I need to find two numbers whose product is 60. I first tried 6 and 10 and 10 is 4 more than 6. So, the card is 10 centimeters long and 6 centimeters wide. The perimeter is 2×10+2×62 \times 10 + 2 \times 6 or 32 centimeters.

Problem 2

Draw 2 rectangles on the grid with a perimeter of 20 units whose areas are different. What is the area of each rectangle?

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Solution

Sample response:

2 rectangles on a dot grid

Problem 3

Draw 2 rectangles on the grid with an area of 30 square units whose perimeters are different. What is the perimeter of each rectangle?

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Solution

Sample response:

2 rectangles on a dot grid

Problem 4

Clare draws a rectangle.

  1. She says that the perimeter of her rectangle is 36 units. What rectangle could Clare have drawn?
  2. Then she says that her rectangle has the largest area possible. What rectangle could Clare have drawn?
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Solution
Sample responses:
  1. It could be a 9 unit by 9 unit square, it could be 10 unit by 8 unit rectangle, or 11 units by 7 units. The length and width have to add up to 18 because 18 and 18 make 36.
  2. I found all of the products and the biggest is 9×9=819 \times 9 = 81. So, Clare must have drawn a square.

Problem 5

Draw a rectangle on the grid but don’t show it to your partner. Give your partner clues to help them guess the perimeter and area of your rectangle. Try not to just tell them the side lengths of your rectangle.

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Solution

Sample responses:

  • A rectangle that is 4 units by 8 units
    • Clue 1: One side is twice as long as the other.
    • Clue 2: The area is more than 20 units but less than 40 square units.
    • Clue 3: One side is 4 units.
  • A rectangle that is 5 units by 7 units
    • Clue 1: One side is 2 units longer than the other.
    • Clue 2: The area is an odd number of square units.
    • Clue 3: The area is less than 40 square units.
    • Clue 4: The area is more than 20 square units.