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Rasheeda sees a garden in a book. She changes the scale because she wants a garden with different dimensions. The figure below shows both scales and a scale drawing of the garden. Book scale: 1 inch = 2 feet. Rasheeda's Scale: 2 inches = 3 feet. A rectangle with length A of 18 inches and width B of 6 inches. Which statements about the gardens are true? Select three options. Length A of the book’s garden is 18 ft. Length A of Rasheeda’s garden is 27 ft. Length B of the book’s garden is 12 ft. Length B of Rasheeda’s garden is 6 ft. Length A of the book’s garden is 9 ft longer than length A of Rasheeda’s garden. Length B of the book’s garden is 3 ft shorter than length B of Rasheeda’s garden.

Question

Rasheeda sees a garden in a book. She changes the scale because she wants a garden with different dimensions. The figure below shows both scales and a scale drawing of the garden.

Book scale: 1 inch = 2 feet. Rasheeda's Scale: 2 inches = 3 feet. A rectangle with length A of 18 inches and width B of 6 inches.

Which statements about the gardens are true? Select three options. Length A of the book’s garden is 18 ft. Length A of Rasheeda’s garden is 27 ft. Length B of the book’s garden is 12 ft. Length B of Rasheeda’s garden is 6 ft. Length A of the book’s garden is 9 ft longer than length A of Rasheeda’s garden. Length B of the book’s garden is 3 ft shorter than length B of Rasheeda’s garden.

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Solution

To answer this question, we need to convert the measurements from the scale to the actual size for both the book's garden and Rasheeda's garden.

  1. Length A of the book’s garden: The book's scale is 1 inch = 2 feet. So, for a length of 18 inches, the actual length would be 18 inches * 2 feet/inch = 36 feet. So, the statement "Length A of the book’s garden is 18 ft" is false.

  2. Length A of Rasheeda’s garden: Rasheeda's scale is 2 inches = 3 feet. So, for a length of 18 inches, the actual length would be 18 inches * (3 feet/2 inches) = 27 feet. So, the statement "Length A of Rasheeda’s garden is 27 ft" is true.

  3. Length B of the book’s garden: The book's scale is 1 inch = 2 feet. So, for a width of 6 inches, the actual width would be 6 inches * 2 feet/inch = 12 feet. So, the statement "Length B of the book’s garden is 12 ft" is true.

  4. Length B of Rasheeda’s garden: Rasheeda's scale is 2 inches = 3 feet. So, for a width of 6 inches, the actual width would be 6 inches * (3 feet/2 inches) = 9 feet. So, the statement "Length B of Rasheeda’s garden is 6 ft" is false.

  5. Length A of the book’s garden is 9 ft longer than length A of Rasheeda’s garden: The length of the book's garden is 36 feet and the length of Rasheeda's garden is 27 feet. So, the book's garden is 36 - 27 = 9 feet longer. So, the statement "Length A of the book’s garden is 9 ft longer than length A of Rasheeda’s garden" is true.

  6. Length B of the book’s garden is 3 ft shorter than length B of Rasheeda’s garden: The width of the book's garden is 12 feet and the width of Rasheeda's garden is 9 feet. So, the book's garden is 12 - 9 = 3 feet longer, not shorter. So, the statement "Length B of the book’s garden is 3 ft shorter than length B of Rasheeda’s garden" is false.

So, the true statements are:

  • Length A of Rasheeda’s garden is 27 ft.
  • Length B of the book’s garden is 12 ft.
  • Length A of the book’s garden is 9 ft longer than length A of Rasheeda’s garden.

This problem has been solved

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